LYONDELL CHEMICAL CO
8-K, 1999-05-12
PETROLEUM REFINING
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<PAGE>
 
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549


                                    FORM 8-K

                                 CURRENT REPORT

                       Pursuant to Section 13 or 15(d) of
                      the Securities Exchange Act of 1934



        Date of Report (date of earliest event reported):  MAY 11, 1999



                           LYONDELL CHEMICAL COMPANY
             (Exact name of registrant as specified in its charter)

<TABLE> 
<CAPTION> 
<S>                        <C>                             <C> 
         1-10145                    DELAWARE                         95-4160558            
(Commission File Number)  (State or other jurisdiction    (IRS Employer Identification No.) 
                               of incorporation)
</TABLE> 
                           

          1221 MCKINNEY STREET                              
     ONE HOUSTON CENTER, SUITE 1600                         
             HOUSTON, TEXAS                                77010   
(Address of principal executive offices)                 (Zip Code) 


      Registrant's telephone number, including area code:  (713) 652-7200

                                 NOT APPLICABLE
         (Former Name or Former Address, if Changed Since Last Report)
<PAGE>
 
ITEM 5.   OTHER EVENTS.

          On May 11, 1999, Lyondell Chemical Company (the "Company") entered
into an Underwriting Agreement (the "Underwriting Agreement") dated May 11, 1999
with Donaldson, Lufkin & Jenrette Securities Corporation, J.P. Morgan
Securities, Inc., Goldman, Sachs & Co., Morgan Stanley & Co. Incorporated,
Salomon Smith Barney Inc. and Schroder & Co., Inc. as representatives of the
several underwriters listed on Schedule I thereto, relating to the offering of
35,000,000 shares of the Company's common stock, par value $1.00 per share,
under its Registration Statement on Form S-3 (Registration No. 333-60429).  The
text of the Underwriting Agreement is being filed as an exhibit to this Current
Report on Form 8-K.

ITEM 7.   FINANCIAL STATEMENTS AND EXHIBITS

     (c)  Exhibits.

     1.1  --   Form of Underwriting Agreement for Common Stock.

                                       2
<PAGE>
 
                                   SIGNATURE



          Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.



                                   LYONDELL CHEMICAL COMPANY


                                   By: /s/ Edward W. Rich
                                       ----------------------------
                                       Edward W. Rich
                                       Vice President, Finance and Treasurer


Date:  May 11, 1999

                                       3

<PAGE>
 
                           LYONDELL CHEMICAL COMPANY


                       35,000,000 SHARES OF COMMON STOCK



                             UNDERWRITING AGREEMENT



MAY 11, 1999
<PAGE>
 
                                               May 11, 1999


Donaldson, Lufkin & Jenrette Securities Corporation
J.P. Morgan Securities Inc.
Goldman, Sachs & Co.
Morgan Stanley & Co. Incorporated
Salomon Smith Barney Inc.
Schroder & Co. Inc.
     As representatives (the 
     "REPRESENTATIVES") of the 
     several Underwriters listed in 
     Schedule I hereto
c/o  Donaldson, Lufkin & Jenrette 
      Securities Corporation
     277 Park Avenue
     New York, New York  10172

Ladies and Gentlemen:

     Lyondell Chemical Company, a Delaware corporation (the "COMPANY"), proposes
to issue and sell to the several Underwriters listed in Schedule I hereto (the
"UNDERWRITERS"), an aggregate of 35,000,000 shares (the "UNDERWRITTEN SHARES")
and, at the election of the Underwriters, up to 5,250,000 additional shares (the
"OPTION SHARES") of common stock, par value $1.00 per share (the "COMMON
STOCK"), of the Company.  The Underwritten Shares and the Option Shares are
herein referred to as the "SHARES".

     The Company has prepared and filed with the Securities and Exchange
Commission (the "COMMISSION") in accordance with the provisions of the
Securities Act of 1933, as amended, and the rules and regulations of the
Commission thereunder (collectively, the "SECURITIES ACT"), a registration
statement (the file number of which is 333-60429) on Form S-3, relating to the
Common Stock and certain other equity and debt securities (the "SHELF
SECURITIES") to be issued from time to time by the Company.  The Company also
has filed with, or proposes to file with, the Commission pursuant to Rule 424
<PAGE>
 
under the Securities Act a prospectus supplement specifically relating to the
Shares.  The registration statement as amended to the date of this Agreement is
hereinafter referred to as the "REGISTRATION STATEMENT" and the related
prospectus covering the Shelf Securities in the form first used to confirm sales
of the Shares is hereinafter referred to as the "BASIC PROSPECTUS".  The Basic
Prospectus as supplemented by the prospectus supplement specifically relating to
the Shares in the form first used to confirm sales of the Shares is hereinafter
referred to as the "PROSPECTUS". If the Company has filed an abbreviated
registration statement pursuant to Rule 462(b) under the Securities Act (the
"RULE 462 REGISTRATION STATEMENT"), then any reference herein to the term
"Registration Statement" shall be deemed to include such Rule 462 Registration
Statement.  Any reference in this Agreement to the Registration Statement, the
Basic Prospectus, any prelimi  nary form of Prospectus (a "PRELIMINARY
PROSPECTUS") previously filed with the Commission pursuant to Rule 424 or the
Prospectus shall be deemed to refer to and include the documents incorporated by
reference therein pursuant to Item 12 of Form S-3 under the Securities Act which
were filed under the Securities Exchange Act of 1934, as amended, and the rules
and regulations of the Commis  sion thereunder (collectively, the "EXCHANGE
ACT") on or before the date of this Agreement or the date of the Basic
Prospectus, any preliminary prospectus or the Prospectus, as the case may be;
and any reference to "amend", "amendment" or "supplement" with respect to the
Registration Statement, the Basic Prospectus, any preliminary prospectus or the
Prospectus shall be deemed to refer to and include any documents filed under the
Exchange Act after the date of this Agreement, or the date of the Basic
Prospectus, any preliminary prospectus or the Prospectus, as the case may be,
which are deemed to be incorporated by reference therein.

     The Company and the Underwriters have agreed that no more than 17,000 of
the Underwritten Shares (the "RESERVED SHARES") shall be reserved for sale by
the Underwriters to certain eligible directors, officers, employees and retirees
of the Company and its subsidiaries, as part of the distribution of the Shares
by the Underwriters, subject to the terms of this Agreement, the applicable
rules, regulations and interpretations of the National Association of Securities
Dealers, Inc. (the "NASD") and all other applicable laws, rules and regulations.

     Concurrently with the offering of the Shares, the Company is offering
$900,000,000 principal amount of its 9% Senior Secured Notes, Series A, due
2007, $1,000,000,000 principal amount of its 9% Senior Secured Notes, Series B,
due 2007, and $500,000,000 principal amount of its 10% Senior Subordinated
Notes due 2009 (collectively, the "NOTES").  The Notes are being offered on a
private placement basis solely to qualified institutional buyers (as such term
is defined in Rule 144A of the Securities Act) pursuant to a separate offering
memorandum, and are being underwritten by a separate syndicate of initial
purchasers  pursuant to a separate purchase agreement dated the date hereof 

                                       2
<PAGE>
 
(as amended, the "NOTES PURCHASE AGREEMENT"). In connection with the Company's
offering of the Notes, the Company, Lyondell Chemical Nederland, Ltd., a
Delaware corporation, Lyondell Chemical Worldwide, Inc., a Delaware corporation
and a wholly owned subsidiary of the Company, and the initial purchasers party
to the Notes Purchase Agreement will enter into a registration rights agreement
(the "REGISTRATION RIGHTS AGREEMENT") dated the date hereof giving the holders
(including subsequent transferees) of the Notes the registration rights set
forth therein for so long as such Notes constitute "Transfer Restricted
Securities" (as defined in the Registration Rights Agreement).

     The Company has heretofore entered into a Credit Agreement dated as of July
23, 1998 among the Company, the lenders party thereto, Morgan Guaranty Trust
Company of New York, as administrative agent, and the syndication agent,
documentation agents, arranger and co-arrangers named therein (as amended, the
"CREDIT AGREEMENT").  The parties to the Credit Agreement have agreed to amend
the Credit Agreement in accordance with Amendment No. 1 dated as of April 1,
1999 ("CREDIT AGREEMENT AMENDMENT NO. 1") and Amendment No. 2 dated as April 16,
1999 ("CREDIT AGREEMENT AMENDMENT NO. 2" and, together with Credit Agreement
Amendment No. 1, the "CREDIT AGREEMENT AMENDMENTS") thereto.  The Credit
Agreement Amendments set forth certain conditions precedent to the effectiveness
thereof, including the sale of the Underwritten Shares and the sale of the
Notes.  The effectiveness of the Credit Agreement Amendments in accordance with
its terms is a condition precedent to the purchase and sale of the Shares under
this Agreement and to the purchase and sale of the Notes under the Notes
Purchase Agreement.

     This Agreement, the Notes Purchase Agreement, the Registration Rights
Agreement and the Credit Agreement Amendments are herein referred to
collectively as the "TRANSACTION DOCUMENTS."

     The Company hereby agrees with the Underwriters as follows:

     1.   The Company agrees to sell the Underwritten Shares to the several
Underwriters as hereinafter provided, and each Underwriter, upon the basis of
the representations and warranties herein contained, but subject to the
conditions hereinafter stated, agrees to purchase, severally and not jointly,
from the Company at a purchase price per share of $18.2875 (the "PURCHASE
PRICE") the number of Underwritten Shares set forth opposite such Underwriter's
name on Schedule I hereto.

     In addition, the Company agrees to sell the Option Shares to the several
Underwriters and the Underwriters shall have the option to purchase at their
election up to 5,250,000 Option Shares for the sole purpose of covering over-
allotments in the sale of the Underwritten Shares. Each Underwriter, on the
basis 

                                       3
<PAGE>
 
of the representations and warranties herein contained, but subject to the
conditions hereinafter stated, shall have the option to purchase, severally and
not jointly, from the Company at the Purchase Price that portion of the number
of Option Shares as to which such election shall have been exercised (to be
adjusted by you so as to eliminate fractional shares) determined by multiplying
such number of Option Shares by a fraction, the numerator of which is the number
of Underwritten Shares set forth opposite such Underwriter's name on Schedule I
hereto and the denominator of which is the total number of Underwritten Shares
set forth in Schedule I hereto, for the sole purpose of covering over-allotments
(if any) in the sale of the Underwritten Shares by the several Underwriters.

     The Underwriters may exercise the option to purchase the Option Shares at
any time (but not more than once) on or before the thirtieth day following the
date of this Agreement, by written notice to the Company from J.P. Morgan
Securities Inc. and Donaldson, Lufkin & Jenrette Securities Corporation on
behalf of the several Underwriters.  Such notice shall set forth the aggregate
number of Option Shares as to which the option is being exercised and the date
and time when the Option Shares are to be delivered and paid for which may be
the same date and time as the Closing Date (as hereinafter defined) but shall
not be earlier than the Closing Date nor later than the tenth full Business Day
(as hereinafter defined) after the date of such notice (unless such time and
date are postponed in accordance with the provisions of Section 9 hereof).  Any
such notice shall be given at least two Business Days prior to the date and time
of delivery specified therein.

     2.   The Company understands that the Underwriters intend (i) to make a
public offering of the Shares as soon after (A) the Registration Statement has
become effective and (B) the parties hereto have executed and delivered this
Agreement, as in the judgment of the Representatives is advisable and (ii)
initially to offer the Shares upon the terms set forth in the Prospectus.

     3.   Payment for the Shares shall be made by wire transfer in immediately
available funds to the account specified to the Representatives by the Company,
in the case of the Underwritten Shares, on May 17, 1999, or at such other time
on the same or such other date, not later than the fifth Business Day
thereafter, as the Representatives and the Company may agree upon in writing or,
in the case of the Option Shares, on the date and time specified by the
Representatives in the written notice of the Underwriters' election to purchase
such Option Shares.  The time and date of such payment for the Underwritten
Shares is referred to herein as the "CLOSING DATE" and the time and date for
such payment for the Option Shares, if other than the Closing Date, is herein
referred to as the "ADDITIONAL CLOSING DATE".  As used herein, the term
"BUSINESS DAY" means any day other than a day on which banks are permitted or
required to be closed in New York City or Houston, Texas.

                                       4
<PAGE>
 
     Payment for the Shares to be purchased on the Closing Date or the
Additional Closing Date, as the case may be, shall be made against delivery to
the Representatives for the respective accounts of the several Underwriters of
the Shares to be purchased on such date registered in such names and in such
denominations as the Representatives shall request in writing not later than two
full Business Days prior to the Closing Date or the Additional Closing Date, as
the case may be, with any transfer taxes payable in connection with the transfer
to the Underwriters of the Shares duly paid by the Company.  Unless the
Underwriters elect to take delivery of the Shares through the book-entry
facilities of the Depository Trust Company, the certificates for the Shares will
be made available for inspection and packaging by the Representatives at the
office of Donaldson, Lufkin & Jenrette Securities Corporation set forth above
not later than 1:00 P.M., New York City time, on the Business Day prior to the
Closing Date or the Additional Closing Date, as the case may be.

     4.   The Company represents and warrants to each Underwriter that:

          (a) no order preventing or suspending the use of any preliminary
     prospectus has been issued by the Commission, and each preliminary
     prospectus filed as part of the Registration Statement as originally filed
     or as part of any amendment thereto, or filed pursuant to Rule 424 under
     the Securities Act, complied when so filed in all material respects with
     the Securities Act, and did not contain an untrue statement of a material
     fact or omit to state a material fact required to be stated therein or
     necessary to make the statements therein, in light of the circumstances
     under which they were made, not misleading; provided that this
     representation and warranty shall not apply to any statements or omissions
     made in reliance upon and in conformity with information relating to any
     Underwriter furnished to the Company in writing by such Underwriter through
     the Representatives expressly for use therein;

          (b) no stop order suspending the effectiveness of the Registration
     Statement has been issued and no proceeding for that purpose has been
     instituted or, to the knowledge of the Company, threatened by the
     Commission; and the Registration Statement and Prospectus (as amended or
     supplemented if the Company shall have furnished any amendments or
     supplements thereto) comply, or will comply, as the case may be, in all
     material respects with the Securities Act and do not and will not, as of
     the applicable effective date as to the Registration Statement and any
     amendment thereto and as of the date of the Prospectus and any amendment or
     supplement thereto, contain any untrue statement of a material fact or omit
     to state any material fact required to be stated therein or necessary to
     make the statements therein not misleading, and the 

                                       5
<PAGE>
 
     Prospectus, as amended or supplemented, if applicable, at the Closing Date
     or Additional Closing Date, as the case may be, will not contain any untrue
     statement of a material fact or omit to state a material fact necessary to
     make the statements therein, in light of the circumstances under which they
     were made, not misleading; except that the foregoing representations and
     warranties shall not apply to statements or omissions in the Registration
     Statement or the Prospectus made in reliance upon and in conformity with
     information relating to any Underwriter furnished to the Company in writing
     by such Underwriter through the Representatives expressly for use therein;

          (c)  the documents incorporated by reference in the Prospectus, when
     they become effective or were filed with the Commission, as the case may
     be, conformed in all material respects to the requirements of the
     Securities Act or the Exchange Act, as applicable, and none of such
     documents contained an untrue statement of a material fact or omitted to
     state a material fact necessary to make the statements therein, in light of
     the circumstances under which they were made, not misleading; and any
     further documents so filed and incorporated by reference in the Prospectus,
     when such documents are filed with the Commission, will conform in all
     material respects to the requirements of the Exchange Act, and will not
     contain an untrue statement of a material fact or omit to state a material
     fact necessary to make the statements therein, in light of the
     circumstances under which they were made, not misleading;

          (d)  the financial statements, and the related notes thereto, included
     or incorporated by reference in the Registration Statement and the
     Prospectus present fairly the consolidated financial position of the
     Company and its consolidated subsidiaries as of the dates indicated and the
     results of their operations and changes in their consolidated cash flows
     for the periods specified; and said financial statements have been prepared
     in conformity with generally accepted accounting principles applied on a
     consistent basis, and the supporting schedules, if any, included or
     incorporated by reference in the Registration Statement present fairly the
     information required to be stated therein; and the pro forma financial
     information, and the related notes thereto, included or incorporated by
     reference in the Registration Statement and the Prospectus has been
     prepared in accordance with the applicable requirements of the Securities
     Act and the Exchange Act, as applicable, and is based upon good faith
     estimates and assumptions believed by the Company to be reasonable;

          (e)  there has not been any change in the capital stock or long-term
     debt of the Company or any of its subsidiaries, or any material adverse
     change in or affecting the business, prospects, condition (financial 

                                       6
<PAGE>
 
     or other), stockholders' equity or results of operations of the Company and
     its subsidiaries, taken as a whole (a "MATERIAL ADVERSE CHANGE"), from that
     set forth or contemplated in the Prospectus (as it stood at the time of
     execution and delivery of this Agreement); and except as set forth or
     contemplated in the Prospectus (as it stood at the time of execution and
     delivery of this Agreement) neither the Company nor any of its Significant
     Joint Ventures (defined below) or subsidiaries has entered into any
     transaction or agreement (whether or not in the ordinary course of
     business) material to the Company and its subsidiaries taken as a whole;

          (f)  the Company has been duly incorporated and is validly existing 
     as a corporation in good standing under the laws of its jurisdiction of
     incorporation with power and authority (corporate and other) to own its
     properties and conduct its business as described in the Prospectus, and has
     been duly qualified as a foreign corporation for the transaction of
     business and is in good standing under the laws of each other jurisdiction
     in which it owns or leases properties, or conducts any business, so as to
     require such qualification, other than where the failure to be so qualified
     or in good standing would not have a material adverse effect on or
     affecting the business, prospects, condition (financial or other),
     stockholders' equity or results of operations of the Company and its
     subsidiaries, taken as a whole (a "MATERIAL ADVERSE EFFECT");

          (g)  each of the Company's subsidiaries has been duly organized and is
     validly existing under the laws of its jurisdiction of organization with
     power and authority (corporate and otherwise) under such laws to own its
     properties and conduct its business as described in the Prospectus, and has
     been duly qualified to do business and is in good standing under the laws
     of each jurisdiction in which it owns or leases properties, or conducts any
     business, so as to require such qualification, other than where the failure
     to be so qualified or in good standing would not have a Material Adverse
     Effect; and all the outstanding shares of capital stock or other ownership
     interests of each subsidiary of the Company have been duly authorized and
     validly issued, are fully-paid and non-assessable, and (except, in the case
     of foreign subsidiaries, for directors' qualifying shares and except as
     otherwise set forth in the Prospectus or pledged under or pursuant to the
     Credit Agreement or pledged as security for the Notes) are owned by the
     Company, directly or indirectly, free and clear of all liens, encumbrances,
     security interests and similar claims;

          (h) each of Equistar Chemicals, LP ("EQUISTAR"), LYONDELL-CITGO
     Refining LP ("LCR") and Lyondell Methanol Company, L.P. ("LYONDELL
     METHANOL", and together with Equistar and LCR, the "SIGNIFICANT JOINT
     VENTURES") has been duly organized and is validly 

                                       7
<PAGE>
 
     existing as a limited partnership under the laws of its jurisdiction of
     organization, with power and authority (partnership and other) to own its
     properties and conduct its business as described in the Prospectus, and has
     been duly qualified for the transaction of business and is in good standing
     under the laws of each jurisdiction in which it owns or leases properties,
     or conducts any business, so as to require such qualification, other than
     where the failure to be so qualified or in good standing would not have a
     Material Adverse Effect; and all the outstanding general and limited
     partnership interests of each Significant Joint Venture have been duly
     authorized and validly issued, are fully-paid and non-assessable (except
     insofar as any such general partnership interest carries with it liability
     for the debts and obligations of the relevant limited partnership), the
     Company owns 41% of the outstanding general and limited partnership
     interests of Equistar, 58.75% of the outstanding general and limited
     partnership interests of LCR and 75% of the outstanding general and limited
     partnership interests of Lyondell Methanol, and (except as otherwise set
     forth in the Prospectus or pledged under or pursuant to the Credit
     Agreement or pledged as security for the Notes) the outstanding general and
     limited partnership interests of the Significant Joint Ventures owned by
     the Company are owned, directly or indirectly, free and clear of all liens,
     encumbrances, security interests and similar claims;

          (i) this Agreement, the Notes Purchase Agreement , the Registration
     Rights Agreement and the Credit Agreement Amendments has each been duly
     authorized, executed and delivered by the Company;

          (j) the Company has an authorized capitalization as set forth in the
     Prospectus and such authorized capital stock conforms as to legal matters
     in all material respects to the description thereof set forth in the
     Prospectus, and all of the outstanding shares of capital stock of the
     Company have been duly authorized and validly issued, are fully-paid and
     non-assessable and are not subject to any pre-emptive or similar rights;
     and, except as described in or expressly contemplated by the Prospectus,
     there are no outstanding rights (including, without limitation, pre-emptive
     rights), warrants or options to acquire, or instruments convertible into or
     exchangeable for, any shares of capital stock or other equity interest in
     the Company or any of its Significant Joint Ventures or subsidiaries, or
     any contract, commitment, agreement, understanding or arrangement of any
     kind relating to the issuance of any capital stock or other equity interest
     of the Company or any such Significant Joint Venture or subsidiary, any
     such convertible or exchangeable securities or any such rights, warrants or
     options;

                                       8
<PAGE>
 
     (k)  the Shares have been duly authorized, and, when issued and delivered
to and paid for by the Underwriters in accordance with the terms of this
Agreement, will be duly issued and will be fully paid and non-assessable and
will conform to the descriptions thereof in the Prospectus; and the issuance of
the Shares is not subject to any preemptive or similar rights;

     (l)  neither the Company nor any of its Significant Joint Ventures or
subsidiaries is, or with the giving of notice or lapse of time or both would be,
in violation of or in default under, its Certificate of Incorporation or By-Laws
or other constitutive documents or any indenture, mortgage, deed of trust, loan
agreement or other agreement or instrument to which the Company or any of its
Significant Joint Ventures or subsidiaries is a party or by which it or any of
them or any of their respective properties is bound, except for violations and
defaults which individually and in the aggregate are not material to the Company
and its subsidiaries taken as a whole; the issue and sale of the Shares to be
sold by the Company hereunder and the performance by the Company of its
obligations under this Agreement and the consummation of the transactions
contemplated herein and in the other Transaction Documents will not conflict
with or result in a breach of any of the terms or provisions of, or constitute a
default under, any indenture, mortgage, deed of trust, loan agreement or other
agreement or instrument to which the Company or any of its Significant Joint
Ventures or subsidiaries is a party or by which the Company or any of its
Significant Joint Ventures or subsidiaries is bound or to which any of the
property or assets of the Company or any of its Significant Joint Ventures or
subsidiaries is subject, nor will any such action result in any violation of the
provisions of the Certificate of Incorporation or the By-Laws of the Company or
any applicable law or statute or any order, rule or regulation of any court or
governmental agency or body having jurisdiction over the Company, its
Significant Joint Ventures or subsidiaries or any of their respective
properties; and no consent, approval, authorization, order, license,
registration or qualification of or with any such court or governmental agency
or body is required for the issue and sale of the Shares to be sold by the
Company hereunder or the consummation by the Company of the transactions
contemplated by this Agreement or in the other Transaction Documents, except
such consents, approvals, authorizations, orders, licenses, registrations or
qualifications as have been obtained under the Securities Act and as may be
required under state securities or Blue Sky Laws in connection with the purchase
and distribution of the Shares by the Underwriters or of the Notes by the
initial purchasers thereof;

                                       9
<PAGE>
 
     (m)  other than as set forth or contemplated in the Prospectus, there are
no legal or governmental investigations, actions, suits or proceedings pending
or, to the knowledge of the Company, threatened against or affecting the Company
or any of its Significant Joint Ventures or subsidiaries or any of their
respective properties or to which the Company or any of its Significant Joint
Ventures or subsidiaries is or may be a party or to which any property of the
Company or any of its Significant Joint Ventures or subsidiaries is or may be
the subject which, if determined adversely to the Company or any of its
Significant Joint Ventures or subsidiaries, could individually or in the
aggregate reasonably be expected to result in a Material Adverse Effect, and, to
the best of the Company's knowledge, no such proceedings are threatened or
contemplated by governmental authorities or threatened by others; and there are
no statutes, regulations, contracts or other documents that are required to be
described in the Registration Statement or Prospectus or to be filed as exhibits
to the Registration Statement that are not described or filed as required;

     (n)  the Company and its Significant Joint Ventures and subsidiaries have
good and marketable title in fee simple to all items of real property and good
title to all personal property owned by them, in each case free and clear of all
liens, encumbrances and defects except such as are described or referred to in
the Prospectus or pledged under or pursuant to the Credit Agreement or pledged
as security for the Notes or such as do not materially affect the value of such
property and do not interfere with the use made or proposed to be made of such
property by the Company and its Significant Joint Ventures and subsidiaries; and
any real property and buildings held under lease by the Company and its
Significant Joint Ventures and subsidiaries are held by them under valid,
existing and enforceable leases with such exceptions as are not material and do
not interfere with the use made or proposed to be made of such property and
buildings by the Company or its Significant Joint Ventures or subsidiaries;

     (o)  no relationship, direct or indirect, exists between or among the
Company or any of its Significant Joint Ventures or subsidiaries on the one
hand, and the directors, officers, stockholders, customers or suppliers of the
Company or any of its Significant Joint Ventures or subsidiaries on the other
hand, which is required by the Securities Act to be described in the
Registration Statement and the Prospectus which is not so described;

     (p)  no person has the right to require the Company to register any
securities for offering and sale under the Securities Act by reason of 

                                       10
<PAGE>
 
the filing of the Registration Statement with the Commission or the issue and
sale of the Shares to be sold by the Company hereunder;

     (q)  the Company is not and, after giving effect to the offering and sale
of the Shares, will not be an "investment company", as such term is defined in
the Investment Company Act of 1940, as amended (the "INVESTMENT COMPANY ACT");

     (r)  the Company has complied with all provisions of Section 517.075,
Florida Statutes (Chapter 92-198, Laws of Florida) relating to doing business
with the Government of Cuba or with any person or affiliate located in Cuba;

     (s)  each of PricewaterhouseCoopers LLP and Deloitte & Touche LLP, who have
certified certain financial statements of the Company and its subsidiaries, are
independent public accountants as required by the Securities Act;

     (t)  the Company and its Significant Joint Ventures and subsidiaries have
filed all federal, state, local and foreign tax returns which have been required
to be filed and have paid all taxes shown thereon and all assessments received
by them or any of them to the extent that such taxes have become due and are not
being contested in good faith;

     (u)  the Company has not taken nor will it take, directly or indirectly,
any action designed to, or that might be reasonably expected to, cause or result
in stabilization or manipulation of the price of the Common Stock of the
Company;

     (v)  each of the Company and its Significant Joint Ventures and
subsidiaries owns, possesses or has obtained all licenses, permits,
certificates, consents, orders, approvals and other authorizations from, and has
made all declarations and filings with, all federal, state, local and other
governmental authorities (including foreign regulatory agencies), all self-
regulatory organizations and all courts and other tribunals, domestic or
foreign, necessary to own or lease, as the case may be, and to operate its
properties and to carry on its business as conducted as of the date hereof,
except such as would not result in a Material Adverse Effect, and neither the
Company nor any such Significant Joint Venture or subsidiary has received any
actual notice of any proceeding relating to revocation or modification of any
such license, permit, certificate, consent, order, approval or other
authorization which, if determined adversely to the Company or any of its
Significant Joint Ventures or subsidiaries could result in a Material Adverse
Effect; and each of the Company and its 

                                       11
<PAGE>
 
     Significant Joint Ventures and subsidiaries is in compliance with all laws
     and regulations relating to the conduct of its business as conducted as of
     the date hereof, except where the failure to so comply would not, singly or
     in the aggregate, result in a Material Adverse Effect;

          (w) there are no existing or, to the best knowledge of the Company,
     threatened labor disputes with the employees of the Company or any of its
     Significant Joint Ventures or subsidiaries which are likely to have a
     Material Adverse Effect;

          (x) the Company and its Significant Joint Ventures and subsidiaries
     (i) are in compliance with any and all applicable foreign, federal, state
     and local laws and regulations relating to the protection of human health
     and safety, the environment or hazardous or toxic substances or wastes,
     pollutants or contaminants ("ENVIRONMENTAL LAWS"), (ii) have received all
     permits, licenses or other approvals required of them under applicable
     Environmental Laws to conduct their respective businesses and (iii) are in
     compliance with all terms and conditions of any such permit, license or
     approval, except where such noncompliance with Environmental Laws, failure
     to receive required permits, licenses or other approvals or failure to
     comply with the terms and conditions of such permits, licenses or approvals
     would not, singly or in the aggregate, have a Material Adverse Effect, and
     except as disclosed in the Registration Statement and the Prospectus; and

          (y) in the ordinary course of its business, the Company conducts a
     periodic review of the effect of Environmental Laws on the business,
     operations and properties of the Company and its Significant Joint Ventures
     and subsidiaries, in the course of which it identifies and evaluates
     associated costs and liabilities (including, without limitation, any
     capital or operating expenditures required for clean-up, closure of
     properties or compliance with Environmental Laws or any permit, license or
     approval, any related constraints on operating activities and any potential
     liabilities to third parties). On the basis of such review, the Company has
     reasonably concluded that such associated costs and liabilities would not,
     singly or in the aggregate, have a Material Adverse Effect, except as
     disclosed in the Registration Statement and the Prospectus.

     5.   The Company covenants and agrees with each of the several Underwriters
as follows:

          (a) to use its best efforts to cause the Registration Statement to
     become effective at the earliest possible time and, if required, to file
     the 

                                       12
<PAGE>
 
     final Prospectus with the Commission within the time periods specified by
     Rule 424(b) and Rule 430A under the Securities Act, and to furnish copies
     of the Prospectus to the Underwriters in New York City prior to 10:00 a.m.,
     New York City time, on the Business Day next succeeding the date of this
     Agreement in such quantities as the Representatives may reasonably request;
 
          (b) to deliver, at the expense of the Company, to the Representatives
     two signed copies of the Registration Statement (as originally filed) and
     each amendment thereto, in each case including exhibits and documents
     incorporated by reference therein, and to each other Underwriter a
     conformed copy of the Registration Statement (as originally filed) and each
     amendment thereto, in each case without exhibits (but including the
     documents incorporated by reference therein), and, during the period
     mentioned in Section 5 below, to each of the Underwriters as many copies of
     the Prospectus (including all amendments and supplements thereto and
     documents incorporated by reference therein) as the Representatives may
     reasonably request;

          (c) before filing any amendment or supplement to the Registration
     Statement or the Prospectus, whether before or after the time the
     Registration Statement becomes effective, to furnish to the Representatives
     a copy of the proposed amendment or supplement for review and not to file
     any such proposed amendment or supplement to which the Representatives
     reasonably object;

          (d) to advise the Representatives promptly, and to confirm such advice
     in writing (i) when the Registration Statement has become effective, (ii)
     when any amendment to the Registration Statement has been filed or becomes
     effective, (iii) when any supplement to the Prospectus or any amended
     Prospectus has been filed and to furnish the Representatives with copies
     thereof, (iv) of any request by the Commission for any amendment to the
     Registration Statement or any amendment or supplement to the Prospectus or
     for any additional information, (v) of the issuance by the Commission of
     any stop order suspending the effectiveness of the Registration Statement
     or of any order preventing or suspending the use of any preliminary
     prospectus or the Prospectus or the initiation or threatening of any
     proceeding for that purpose, (vi) of the occurrence of any event, within
     the period referenced in Section 5 below, as a result of which the
     Prospectus as then amended or supplemented would include an untrue
     statement of a material fact or omit to state any material fact necessary
     in order to make the statements therein, in the light of the circumstances
     when the Prospectus is delivered to a purchaser, not misleading, and (vii)
     of the receipt by the Company of any

                                       13
<PAGE>
 
     notification with respect to any suspension of the qualification of the
     Shares for offer and sale in any jurisdiction or the initiation or
     threatening of any proceeding for such purpose; and to use its best efforts
     to prevent the issuance of any such stop order, or of any order preventing
     or suspending the use of any preliminary prospectus or the Prospectus, or
     of any order suspending any such qualification of the Shares, or
     notification of any such order thereof and, if issued, to obtain as soon as
     possible the withdrawal thereof;

          (e) if, during such period of time after the first date of the public
     offering of the Shares as in the opinion of counsel for the Underwriters a
     prospectus relating to the Shares is required by law to be delivered in
     connection with sales by the Underwriters or any dealer, any event shall
     occur as a result of which it is necessary to amend or supplement the
     Prospectus in order to make the statements therein, in light of the
     circumstances when the Prospectus is delivered to a purchaser, not
     misleading, or if it is necessary to amend or supplement the Prospectus to
     comply with law, forthwith to prepare and furnish, at the expense of the
     Company, to the Underwriters and to the dealers (whose names and addresses
     the Representatives will furnish to the Company) to which Shares may have
     been sold by the Representatives on behalf of the Underwriters and to any
     other dealers upon request, such amendments or supplements to the
     Prospectus as may be necessary so that the statements in the Prospectus as
     so amended or supplemented will not, in the light of the circumstances when
     the Prospectus is delivered to a purchaser, be misleading or so that the
     Prospectus will comply with law;

          (f) to endeavor to qualify the Shares for offer and sale under the
     securities or Blue Sky laws of such jurisdictions as the Representatives
     shall reasonably request and to continue such qualification in effect so
     long as reasonably required for distribution of the Shares; provided that
     the Company shall not be required to (x) file a general consent to service
     of process, (y) subject itself to taxation or (z) qualify as a foreign
     corporation in any jurisdiction in which it is not otherwise required to do
     so;

          (g) to make generally available to its security holders and to the
     Representatives as soon as practicable an earnings statement covering a
     period of at least twelve months beginning with the first fiscal quarter of
     the Company occurring after the effective date of the Registration
     Statement, which shall satisfy the provisions of Section 11(a) of the
     Securities Act and Rule 158 of the Commission promulgated thereunder;

                                       14
<PAGE>
 
          (h) for a period of five years, to furnish to the Representatives
     copies of all reports or other communications (financial or other)
     furnished to holders of the Shares, and copies of any reports and financial
     statements furnished to or filed with the Commission or any national
     securities exchange;

          (i) for a period of 90 days after the date of the public offering of
     the Shares not to (x) offer, pledge, announce the intention to sell, sell,
     contract to sell, sell any option or contract to purchase, purchase any
     option or contract to sell, grant any option, right or warrant to purchase
     or otherwise transfer or dispose of, directly or indirectly, any shares of
     Common Stock or any securities convertible into or exercisable or
     exchangeable for Common Stock or (y) enter into any swap or other agreement
     that transfers, in whole or in part, any of the economic consequences of
     ownership of the Common Stock, whether any such transaction described in
     clause (x) or (y) above is to be settled by delivery of Common Stock or
     such other securities, in cash or otherwise without the prior written
     consent of Donaldson, Lufkin & Jenrette Securities Corporation, other than
     the Shares to be sold by the Company hereunder and any shares of Common
     Stock of the Company issued upon the exercise of options granted under
     existing employee stock option plans;

          (j) to use the net proceeds received by the Company from the sale of
     the Shares pursuant to this Agreement in the manner specified in the
     Prospectus under caption "Use of Proceeds";

          (k) to use its best efforts to list, subject to notice of issuance,
     the Shares on the New York Stock Exchange;

          (l) whether or not the transactions contemplated in this Agreement are
     consummated or this Agreement is terminated, to pay or cause to be paid all
     costs and expenses incident to the performance of its obligations
     hereunder, including without limiting the generality of the foregoing, all
     costs and expenses (i) incident to the preparation, registration, transfer,
     execution and delivery of the Shares, including any transfer or other taxes
     payable thereon, (ii) incident to the preparation, printing and filing
     under the Securities Act of the Registration Statement, the Prospectus and
     any preliminary prospectus (including in each case all exhibits, amendments
     and supplements thereto), (iii) incurred in connection with the
     registration or qualification of the Shares under the laws of such
     jurisdictions as the Representatives may designate (including fees of
     counsel for the Underwriters and their disbursements), (iv) in connection
     with the listing of the Shares on the New York Stock Exchange, (v) related
     to the filing with, and clearance of the offering by, 

                                       15
<PAGE>
 
     the NASD (including fees of counsel for the Underwriters and their
     disbursements), (vi) in connection with the printing (including word
     processing and duplication costs) and delivery of this Agreement, the
     Preliminary and Supplemental Blue Sky Memoranda and the furnishing to the
     Underwriters and dealers of copies of the Registration Statement and the
     Prospectus, including mailing and shipping, as herein provided, (vii) any
     expenses incurred by the Company in connection with a "road show"
     presentation to potential investors, (viii) the cost of preparing stock
     certificates, (ix) the cost and charges of any transfer agent and any
     registrar, and (x) in connection with matters related to the Reserved
     Shares which are designated by the Company for sale to certain directors,
     officers, employees and retirees of the Company, all costs and expenses of
     the Underwriters, including the fees and disbursements of counsel for the
     Underwriters and all stamp duties, similar taxes or duties or other taxes,
     if any; and

          (m) to the extent required by the rules of the NASD, to ensure that
     the Reserved Shares will be restricted as required by the NASD or the NASD
     rules from sale, transfer, assignment, pledge or hypothecation for a period
     of three months following the date of this Agreement. The Underwriters will
     notify the Company as to which purchasers of Reserved Shares will need to
     be so restricted. At the request of the Underwriters, the Company will
     direct the transfer agent to place a stop transfer restriction upon such
     Reserved Shares for such period of time. Should the Company release, or
     seek to release, from such restrictions any of the Reserved Shares, the
     Company agrees to reimburse the Underwriters for any reasonable expenses
     (including, without limitation, legal expenses) they incur in connection
     with such release.

     6.   The several obligations of the Underwriters hereunder to purchase the
Shares on the Closing Date or the Additional Closing Date, as the case may be,
are subject to the performance by the Company of its obligations hereunder and
to the following additional conditions:

          (a) the Registration Statement shall have become effective (or if a
     post-effective amendment is required to be filed under the Securities Act,
     such post-effective amendment shall have become effective) not later than
     5:00 P.M., New York City time, on the date hereof; and no stop order
     suspending the effectiveness of the Registration Statement or any post-
     effective amendment shall be in effect, and no proceedings for such purpose
     shall be pending before or threatened by the Commission; the Prospectus
     shall have been filed with the Commission pursuant to Rule 424(b) within
     the applicable time period prescribed for such filing by the rules and
     regulations under the Securities Act and in accordance with 

                                       16
<PAGE>
 
     Section 5(a) hereof; and all requests of the Representatives for additional
     information shall have been complied with to the reasonable satisfaction of
     the Representatives;

          (b) the representations and warranties of the Company contained herein
     are true and correct on and as of the Closing Date or the Additional
     Closing Date, as the case may be, as if made on and as of the Closing Date
     or the Additional Closing Date, as the case may be, and the Company shall
     have complied in all material respects with all agreements and all
     conditions on its part to be performed or satisfied hereunder at or prior
     to the Closing Date or the Additional Closing Date, as the case may be;

          (c) subsequent to the execution and delivery of this Agreement and
     prior to the Closing Date or the Additional Closing Date, as the case may
     be, there shall not have occurred any downgrading, nor shall any notice
     have been given of (i) any downgrading, (ii any intended or potential
     downgrading or (ii any review or possible change that does not indicate an
     improvement, in the rating accorded any securities of or guaranteed by the
     Company by any "nationally recognized statistical rating organization", as
     such term is defined for purposes of Rule 436(g)(2) under the Securities
     Act;

          (d) there shall not have been any change in the capital stock or long-
     term debt of the Company or any of its Significant Joint Ventures or
     subsidiaries or any Material Adverse Change from that set forth or
     contemplated in the Prospectus (as it stood at the time of execution and
     delivery of this Agreement), the effect of which in the judgment of the
     Representatives makes it impracticable or inadvisable to proceed with the
     public offering or the delivery of the Shares on the Closing Date or the
     Additional Closing Date, as the case may be, on the terms and in the manner
     contemplated in the Prospectus (as it stood at the time of execution and
     delivery of this Agreement);

          (e) the Representatives shall have received on and as of the Closing
     Date or the Additional Closing Date, as the case may be, a certificate of
     an executive officer of the Company, with specific knowledge about the
     Company's financial matters, satisfactory to the Representatives to the
     effect set forth in Sections 6, 6 and 6 and to the further effect that
     there has not occurred any Material Adverse Change from that set forth or
     contemplated in the Prospectus (as it stood at the time of execution and
     delivery of this Agreement);

          (f) Baker & Botts, L.L.P., outside counsel for the Company, shall have
     furnished to the Representatives its written opinion, dated the 

                                       17
<PAGE>
 
     Closing Date or the Additional Closing Date, as the case may be, in form
     and substance reasonably satisfactory to the Representatives, to the effect
     that:

              (i) the Company is a corporation duly incorporated and validly
          existing in good standing under the laws of the State of Delaware,
          with corporate power and authority under such laws to own its
          properties and conduct its business as described in the Prospectus;

              (ii) this Agreement has been duly authorized, executed and
          delivered by the Company;

              (iii) the authorized capital stock of the Company conforms as to
          legal matters in all material respects to the description thereof
          contained in the Prospectus;

              (iv) the Shares to be issued and sold hereunder have been duly
          authorized by the Company, and when delivered to and paid for by the
          Underwriters in accordance with the terms of this Agreement, will be
          validly issued, fully paid and non-assessable and the issuance of the
          Shares is not subject to any preemptive rights of any stockholder of
          the Company or, to the knowledge of such counsel, of any other person;

              (v) such counsel does not know of any statutes, regulations,
          contracts or other documents that are required to be described in the
          Registration Statement or Prospectus or to be filed as exhibits to the
          Registration Statement that are not described or filed as required;

              (vi) the Registration Statement and the Prospectus and any
          amendments and supplements thereto, excluding the documents
          incorporated by reference therein (other than the financial statements
          and related schedules and other financial and statistical data
          therein, as to which such counsel need express no opinion) as of the
          dates they became effective or were filed with the Commission, as the
          case may be, appear on their face to be appropriately responsive in
          all material respects to the requirements of the Securities Act;

              (vii) the documents incorporated by reference in the Prospectus or
          any further amendment or supplement thereto made by the Company prior
          to the Closing Date or the Additional 

                                       18
<PAGE>
 
          Closing Date, as the case may be (other than the financial statements
          and related schedules and other financial and statistical data
          therein, as to which such counsel need express no opinion), when they
          became effective or were filed under the Exchange Act with the
          Commission, as the case may be, appear on their face to be
          appropriately responsive in all material respects to the requirements
          of the Securities Act or the Exchange Act, as applicable, and the
          rules and regulations of the Commission thereunder;

              (viii) the issue and sale of the Shares being delivered on the
          Closing Date or the Additional Closing Date, as the case may be, and
          the performance by the Company of its obligations under this Agreement
          and the consummation of the transactions contemplated herein and in
          the other Transaction Documents will not (1) result in any violation
          of the provisions of (a) the Certificate of Incorporation or the By-
          Laws of the Company or (b) any law or statute or any order, rule or
          regulation of any court or governmental agency or body having
          jurisdiction over the Company, its Significant Joint Ventures or
          subsidiaries or any of their respective properties or (2) conflict
          with or result in a breach of any of the terms or provisions of, or
          constitute a default under, the Credit Agreement;

              (ix) no consent, approval, authorization, order, license,
          registration or qualification of or with any court or governmental
          agency or body is required for the issuance by the Company of the
          Shares to be sold by it hereunder or the consummation by the Company
          of the other transactions contemplated by this Agreement or the other
          Transaction Documents, except such consents, approvals,
          authorizations, orders, licenses, registrations or qualifications as
          have been obtained under the Securities Act and as may be required
          under state securities or Blue Sky laws in connection with the
          purchase and distribution of the Shares by the Underwriters; and

              (x) the Company is not and, after giving effect to the offering
          and sale of the Shares, will not be an "investment company", as such
          term is defined in the Investment Company Act.

                  Such counsel shall also state that they have participated in
          conferences with officers and other representatives of the Company,
          representatives of the independent accountants of the Company and
          representatives of the Underwriters and their 

                                       19
<PAGE>
 
          counsel at which the contents of the Registration Statement and the
          Prospectus and related matters were discussed; and, although such
          counsel did not independently verify such information and is not
          passing upon, and does not assume any responsibility for, the
          accuracy, completeness or fairness of the statements contained in the
          Registration Statement and the Prospectus, on the basis of the
          foregoing (relying as to materiality, to the extent such counsel deems
          reasonable, upon officers and other representatives of the Company),
          no facts have come to the attention of such counsel to lead such
          counsel to believe that (a) the Registration Statement (other than the
          financial statements, the notes thereto and the auditors' reports
          thereon and the other financial, statistical and accounting
          information contained therein or omitted therefrom, as to which such
          counsel has not been asked to comment), at its effective date,
          contained an untrue statement of a material fact or omitted to state a
          material fact required to be stated therein or necessary to make the
          statements therein not misleading or (b) the Prospectus (other than
          the financial statements, the notes thereto and the auditors' reports
          thereon and the other financial, statistical and accounting
          information contained therein or omitted therefrom, as to which such
          counsel has not been asked to comment), at the time the Prospectus was
          issued, or at the Closing Date, contained or contains an untrue
          statement of a material fact or omitted or omits to state a material
          fact necessary in order to make the statements therein, in the light
          of the circumstances under which they were made, not misleading.

              Such counsel may state that the opinions expressed are based on
          and are limited to the laws of the State of Texas, the General
          Corporation Law of the State of Delaware, the contract law of the
          State of New York and the federal laws of the United States, as
          currently in effect.

          (g) Robert J. Millstone, Esq., general counsel for the Company, shall
     have furnished to the Representatives his written opinion, dated the
     Closing Date or the Additional Closing Date, as the case may be, in form
     and substance reasonably satisfactory to the Representatives, to the effect
     that:

              (i) the shares of capital stock of the Company outstanding prior
          to the issuance of the Shares to be sold hereunder have been duly
          authorized and are validly issued, fully paid and non-assessable;

                                       20
<PAGE>
 
              (ii) the Company has been duly qualified to do business and is in
          good standing as a foreign corporation under the laws of each
          jurisdiction in which it owns or leases properties, or conducts any
          business, so as to require such qualification, other than where the
          failure to be so qualified or in good standing would not have a
          Material Adverse Effect;

              (iii) each of the Company's subsidiaries has been duly organized
          and is validly existing under the laws of its jurisdiction of
          organization with power and authority (corporate and otherwise) under
          such laws to own its properties and conduct its business as described
          in the Prospectus and has been duly qualified to do business and is in
          good standing under the laws of each jurisdiction in which it owns or
          leases properties, or conducts any business, so as to require such
          qualification, other than where the failure to be so qualified and in
          good standing would not have a Material Adverse Effect; and all of the
          outstanding shares of capital stock or other ownership interests of
          each subsidiary have been duly and validly authorized and issued, are
          fully paid and non-assessable, and (except, in the case of foreign
          subsidiaries, for directors' qualifying shares and except as otherwise
          set forth in the Prospectus or pledged under or pursuant to the Credit
          Agreement or pledged as security for the Notes) are owned by the
          Company, directly or indirectly, free and clear of all liens,
          encumbrances, security interests and similar claims;

              (iv) each of the Significant Joint Ventures has been duly
          organized and is validly existing as a limited partnership under the
          laws of Delaware, with power and authority under its partnership
          agreement and the law of the State of Delaware to own its properties
          and conduct its business as described in the Prospectus, and has been
          duly qualified for the transaction of business and is in good standing
          under the laws of each jurisdiction in which it owns or leases
          properties, or conducts any business, so as to require such
          qualification, other than where the failure to be so qualified or in
          good standing would not have a Material Adverse Effect; and all the
          outstanding general and limited partnership interests of each
          Significant Joint Venture have been duly authorized and validly
          issued, are fully-paid and non-assessable (except insofar as any such
          general partnership interest carries with it liability for the debts
          and obligations of the relevant limited partnership). The Company owns
          41% of the outstanding general and limited partnership interests of
          Equistar, 58.75% of the 

                                       21
<PAGE>
 
          outstanding general and limited partnership interests of LCR and 75%
          of the outstanding general and limited partnership interests of
          Lyondell Methanol, and (except as otherwise set forth in the
          Prospectus or pledged under or pursuant to the Credit Agreement or
          pledged as security for the Notes) the outstanding general and limited
          partnership interests of the Significant Joint Ventures owned by the
          Company owned by the Company are owned, directly or indirectly, free
          and clear of all liens, encumbrances, security interests and similar
          claims;

              (v) other than as set forth or contemplated in the Prospectus, to
          the best of such counsel's knowledge, there are no legal or
          governmental investigations, actions, suits or proceedings pending or
          threatened or contemplated against the Company, its subsidiaries, LCR
          or Lyondell Methanol or any of their respective properties or to which
          the Company, its subsidiaries, LCR or Lyondell Methanol is or may be a
          party or to which any property of the Company, its subsidiaries, LCR
          or Lyondell Methanol is or may be the subject that, if determined
          adversely to the Company, its subsidiaries, LCR or Lyondell Methanol,
          could individually or in the aggregate reasonably be expected to have
          a Material Adverse Effect;

              (vi) such counsel does not know of any statutes, regulations,
          contracts or other documents that are required to be described in the
          Registration Statement or Prospectus or to be filed as exhibits to the
          Registration Statement that are not described or filed as required;

              (vii) none of the Company, its subsidiaries, LCR or Lyondell
          Methanol is, or with the giving of notice or lapse of time or both
          would be, in violation of or in default under its Certificate of
          Incorporation or By-Laws or other constitutive documents, or to the
          best of such counsel's knowledge, any indenture, mortgage, deed of
          trust, loan agreement or other agreement or instrument to which the
          Company, its subsidiaries, LCR or Lyondell Methanol is a party or by
          which it or any of them or any of their respective properties is
          bound, except for violations and defaults which individually and in
          the aggregate are not material to the Company and its subsidiaries
          taken as a whole;

              (viii) the issue and sale of the Shares being delivered on the
          Closing Date or the Additional Closing Date, as the case may be, and
          the performance by the Company of its obligations under this Agreement
          and the consummation of the transactions contemplated 

                                       22
<PAGE>
 
          herein and in the other Transaction Documents will not conflict with
          or result in a breach of any of the terms or provisions of, or
          constitute a default under, any indenture, mortgage, deed of trust,
          loan agreement or other agreement or instrument known to such counsel
          to which the Company, its subsidiaries, LCR or Lyondell Methanol is a
          party or by which the Company, its subsidiaries, LCR or Lyondell
          Methanol is bound or to which any of the property or assets of the
          Company, its subsidiaries, LCR or Lyondell Methanol is subject, nor
          will any such action result in any violation of the provisions of the
          Certificate of Incorporation or the By-Laws of the Company or, to the
          knowledge of such counsel, any applicable law or statute or any order,
          rule or regulation of any court or governmental agency or body having
          jurisdiction over the Company, its subsidiaries, LCR or Lyondell
          Methanol or any of their respective properties; and

              (ix) each of the Company, its subsidiaries, LCR or Lyondell
          Methanol owns, possesses or has obtained all licenses, permits,
          certificates, consents, orders, approvals and other authorizations
          from, and has made all declarations and filings with, all federal,
          state, local and other governmental authorities (including foreign
          regulatory agencies), all self-regulatory organizations and all courts
          and other tribunals, domestic or foreign, necessary to own or lease,
          as the case may be, and to operate its properties and to carry on its
          business as conducted as of the date hereof, except such as could not
          reasonably be expected to have a Material Adverse Effect, and to the
          best of such counsel's knowledge, none of the Company, its
          subsidiaries, LCR or Lyondell Methanol has received any actual notice
          of any proceeding relating to revocation or modification of any such
          license, permit, certificate, consent, order, approval or other
          authorization which, if determined adversely to the Company, its
          subsidiaries, LCR or Lyondell Methanol could reasonably be expected to
          have a Material Adverse Effect, and each of the Company, its
          subsidiaries, LCR or Lyondell Methanol is in compliance with all laws
          and regulations relating to the conduct of its business as conducted
          as of the date hereof, except where the failure to so comply could not
          reasonably be expected to have a Material Adverse Effect.

              Such counsel shall also state that he has participated in
          conferences with officers and other representatives of the Company,
          and persons under his direction or control have participated in
          conferences with officers and other representatives 

                                       23
<PAGE>
 
          of the Company, representatives of the independent accountants of the
          Company and representatives of the Underwriters and their counsel at
          which the contents of the Registration Statement and the Prospectus
          and related matters were discussed; and, although he did not
          independently verify such information and is not passing upon, and
          does not assume any responsibility for, the accuracy, completeness or
          fairness of the statements contained in the Registration Statement and
          the Prospectus, on the basis of the foregoing (relying as to
          materiality, to the extent such counsel deems reasonable, upon
          officers and other representatives of the Company), no facts have come
          to his attention to lead him to believe that (a) the Registration
          Statement (other than the financial statements, the notes thereto and
          the auditors' reports thereon and the other financial, statistical and
          accounting information contained therein or omitted therefrom, as to
          which such counsel has not been asked to comment), at its effective
          date, contained an untrue statement of a material fact or omitted to
          state a material fact required to be stated therein or necessary to
          make the statements therein not misleading or (b) the Prospectus
          (other than the financial statements, the notes thereto and the
          auditors' reports thereon and the other financial, statistical and
          accounting information contained therein or omitted therefrom, as to
          which such counsel has not been asked to comment), at the time the
          Prospectus was issued, or at the Closing Date, contained or contains
          an untrue statement of a material fact or omitted or omits to state a
          material fact necessary in order to make the statements therein, in
          the light of the circumstances under which they were made, not
          misleading.

              Such counsel may state that the opinions expressed are based on
          and are limited to the laws of the United States, the General
          Corporation Law of the State of Delaware and the Revised Uniform
          Limited Partnership Act of the State of Delaware, as currently in
          effect.

          (h) Gerald A. O'Brien, Esq., general counsel for Equistar, shall have
     furnished to the Representatives his written opinion, dated the Closing
     Date or the Additional Closing Date, as the case may be, in form and
     substance reasonably satisfactory to the Representatives, to the effect
     that:

              (i) other than as set forth or contemplated in the Prospectus, to
          the best of such counsel's knowledge, there are no legal or
          governmental investigations, actions, suits or proceedings 

                                       24
<PAGE>
 
          pending or threatened or contemplated against Equistar or any of its
          subsidiaries or any of their respective properties or to which
          Equistar or any of its subsidiaries is or may be a party or to which
          any property of Equistar or any of its subsidiaries is or may be the
          subject which, if determined adversely to Equistar or its
          subsidiaries, could individually or in the aggregate reasonably be
          expected to have a Material Adverse Effect;

              (ii) neither Equistar nor any of its subsidiaries is, or with the
          giving of notice or lapse of time or both would be, in violation of or
          in default under its Limited Partnership Agreement or other
          constitutive documents, or to the best of such counsel's knowledge,
          any indenture, mortgage, deed of trust, loan agreement or other
          agreement or instrument to which Equistar or any of its subsidiaries
          is a party or by which it or any of them or any of their respective
          properties is bound, except for violations and defaults which
          individually and in the aggregate are not material to Equistar and its
          subsidiaries taken as a whole;

              (iii) the issue and sale of the Shares being delivered on the
          Closing Date or the Additional Closing Date, as the case may be, and
          the performance by Equistar and its subsidiaries of its obligations
          under this Agreement and the consummation of the transactions
          contemplated herein and in the other Transaction Documents will not
          conflict with or result in a breach of any of the terms or provisions
          of, or constitute a default under, any indenture, mortgage, deed of
          trust, loan agreement or other agreement or instrument known to such
          counsel to which Equistar or any of its subsidiaries is a party or by
          which Equistar or any of its subsidiaries is bound or to which any of
          the property or assets of Equistar or any of its subsidiaries is
          subject, nor will any such action result in any violation of the
          provisions of the Limited Partnership Agreement of Equistar or, to the
          knowledge of such counsel, any applicable law or statute or any order,
          rule or regulation of any court or governmental agency or body having
          jurisdiction over Equistar, its subsidiaries or any of their
          respective properties; and

              (iv) each of Equistar and its subsidiaries owns, possesses or has
          obtained all licenses, permits, certificates, consents, orders,
          approvals and other authorizations from, and has made all declarations
          and filings with, all federal, state, local and other governmental
          authorities (including foreign regulatory agencies), all self-
          regulatory organizations and all courts and other tribunals, 

                                       25
<PAGE>
 
          domestic or foreign, necessary to own or lease, as the case may be,
          and to operate its properties and to carry on its business as
          conducted as of the date hereof, except such as could not reasonably
          be expected to have a Material Adverse Effect, and to the best of such
          counsel's knowledge, neither Equistar nor any of its subsidiaries has
          received any actual notice of any proceeding relating to revocation or
          modification of any such license, permit, certificate, consent, order,
          approval or other authorization which, if determined adversely to
          Equistar or any of its subsidiaries could reasonably be expected to
          have a Material Adverse Effect, and each of Equistar and its
          subsidiaries is in compliance with all laws and regulations relating
          to the conduct of its business as conducted as of the date hereof,
          except where the failure to so comply could not reasonably be expected
          to have a Material Adverse Effect.

              Such counsel shall also state that the opinions expressed are
          based on and are limited to the laws of the United States, the General
          Corporation Law of the State of Delaware and the Revised Uniform
          Limited Partnership Act of the State of Delaware, as currently in
          effect.

     In rendering such opinions, Baker & Botts, L.L.P., Mr. Millstone and Mr.
O'Brien may rely as to matters of fact, to the extent such counsel deems proper,
on certificates of responsible officers of the Company and certificates or other
written statements of officials of jurisdictions having custody of documents
respecting the corporate existence or good standing of the Company.

     The opinions of Baker & Botts, L.L.P., Mr. Millstone and Mr. O'Brien
described above shall be rendered to the Underwriters at the request of the
Company and shall so state therein.

          (i) the Representatives shall have received, at the time this
     Agreement is executed and at the Closing Date, letters dated the date
     hereof or the Closing Date, as the case may be, in form and substance
     satisfactory to you from PricewaterhouseCoopers LLP and Deloitte & Touche
     LLP letters, independent public accountants, containing statements and
     information of the type customarily included in accountants' "comfort
     letters" to underwriters with respect to the financial statements and
     certain financial information contained in the Registration Statement and
     the Prospectus;

          (j) the Representatives shall have received on and as of the Closing
     Date or Additional Closing Date, as the case may be, an opinion of Davis
     Polk & Wardwell, counsel to the Underwriters, with respect to 

                                       26
<PAGE>
 
     the due authorization and valid issuance of the Shares, the Registration
     Statement, the Prospectus and other related matters as the Representatives
     may reasonably request, and such counsel shall have received such papers
     and information as they may reasonably request to enable them to pass upon
     such matters;

          (k) the Credit Agreement Amendments shall have been authorized,
     executed and delivered by each party thereto and shall constitute a valid
     and binding agreement of each party thereto, and all conditions precedent
     to the effectiveness of the Credit Agreement Amendments, other than the
     conditions set forth in Section 26(i) of Credit Agreement Amendment No. 1
     and Section 15(i) of Credit Agreement Amendment No. 2 thereof relating to
     the issuances of securities described therein, shall have been either
     satisfied or waived by the lenders party thereto;

          (l) the Notes Purchase Agreement shall have been authorized, executed
     and delivered by each party thereto and shall constitute a valid and
     binding agreement of each party thereto, and all conditions precedent to
     the purchase and sale of the Notes pursuant to the Notes Purchase
     Agreement, other than the conditions set forth in Section 9(p) thereof
     relating to the issuance of the Shares under this Agreement, shall have
     been either satisfied or waived by the initial purchasers party thereto;

          (m) the Registration Rights Agreement shall have been authorized,
     executed and delivered by each party thereto and shall constitute a valid
     and binding agreement of each party thereto, enforceable in accordance with
     its terms, except as (x) the enforceability thereof may be limited by
     bankruptcy, insolvency or similar laws affecting creditors' rights
     generally and (y) rights of acceleration and the availability of equitable
     remedies may be limited by equitable principles of general applicability
     (which principles may include implied duties of good faith and fair
     dealing);

          (n) the Shares shall have been approved for listing on the New York
     Stock Exchange, subject to official notice of issuance;

          (o) on or prior to the Closing Date or Additional Closing Date, as the
     case may be, the Company shall have furnished to the Representatives such
     further certificates and documents as the Representatives shall reasonably
     request; and

          (p) The "lock-up" agreements, each substantially in the form of
     Exhibit A hereto, between you and certain directors of the Company 

                                       27
<PAGE>
 
     relating to sales and certain other dispositions of shares of Common Stock
     or certain other securities, delivered to you on or before the date hereof,
     shall be in full force and effect on the Closing Date or Additional Closing
     Date, as the case may be.

     7.   The Company agrees to indemnify and hold harmless each Underwriter and
each person, if any, who controls any Underwriter within the meaning of either
Section 15 of the Securities Act or Section 20 of the Exchange Act,  from and
against any and all losses, claims, damages and liabilities (including, without
limitation, the legal fees and other expenses incurred in connection with any
suit, action or proceeding or any claim asserted) caused by any untrue statement
or alleged untrue statement of a material fact contained in the Registration
Statement or the Prospectus (as amended or supplemented if the Company shall
have furnished any amendments or supplements thereto) or any preliminary
prospectus, or caused by any omission or alleged omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading, except insofar as such losses, claims, damages or
liabilities are caused by any untrue statement or omission or alleged untrue
statement or omission made in reliance upon and in conformity with information
relating to any Underwriter furnished to the Company in writing by such
Underwriter through the Representatives expressly for use therein; provided,
however, that with respect to any such untrue statement in or omission from the
preliminary prospectus, the indemnity agreement contained in this Section 7
shall not inure to the benefit of any such Underwriter to the extent that the
sale to the person asserting any such loss, claim, damage or liability was an
initial resale by such Underwriter and any such loss, claim, damage or liability
of or with respect to such Underwriter results from the fact that both (A) to
the extent required by applicable law, a copy of the Prospectus was not sent or
given to such person at or prior to the written confirmation of the sale of the
Shares to such person and (B) the untrue statement in or omission from the
preliminary prospectus was corrected in the Prospectus unless, in either case,
such failure to deliver the Prospectus was a result of noncompliance by the
Company with Section 5(b).

     In connection with the offer and sale of the Reserved Shares, the Company
agrees, promptly upon a request in writing, to indemnify and hold harmless the
Underwriters from and against any and all losses, claims, damages and
liabilities incurred by them as a result of the failure of eligible persons to
pay for and accept delivery of Reserved Shares which, by the end of the first
business day following the date of this Agreement, were subject to a properly
confirmed agreement to purchase.

     Each Underwriter agrees, severally and not jointly, to indemnify and hold
harmless the Company, its directors, its officers who sign the Registration
Statement and each person who controls the Company within the meaning of 

                                       28
<PAGE>
 
Section 15 of the Securities Act and Section 20 of the Exchange Act to the same
extent as the foregoing indemnity from the Company to each Underwriter, but only
with reference to information relating to such Underwriter furnished to the
Company in writing by such Underwriter through the Representatives expressly for
use in the Registration Statement, the Prospectus, any amendment or supple ment
thereto, or any preliminary prospectus.

     If any suit, action, proceeding (including any governmental or regulatory
investigation), claim or demand shall be brought or asserted against any person
in respect of which indemnity may be sought pursuant to the preceding paragraphs
of this Section 7, such person (the "INDEMNIFIED PERSON") shall promptly notify
the person or persons against whom such indemnity may be sought (each an
"INDEMNIFYING PERSON") in writing, and such Indemnifying Persons, upon request
of the Indemnified Person, shall retain counsel reasonably satisfactory to the
Indemnified Person to represent the Indemnified Person and any others the
Indemnifying Persons may designate in such proceeding and shall pay the fees and
expenses of such counsel related to such proceeding. In any such proceeding, any
Indemnified Person shall have the right to retain its own counsel, but the fees
and expenses of such counsel shall be at the expense of such Indemnified Person
and not the Indemnifying Persons unless (i) the Indemnifying Persons and the
Indemnified Person shall have mutually agreed to the contrary, (ii) the
Indemnifying Persons has failed within a reasonable time to retain counsel
reasonably satisfactory to the Indemnified Person or (iii) the named parties in
any such proceeding (including any impleaded parties) include both an
Indemnifying Person and the Indemnified Person and representation of both
parties by the same counsel would be inappropriate due to actual or potential
differing interests between them. It is understood that no Indemnifying Person
shall, in connection with any proceeding or related proceeding in the same
jurisdiction, be liable for the fees and expenses of more than one separate firm
(in addition to any local counsel) for all Indemnified Persons, and that all
such fees and expenses shall be reimbursed as they are incurred.  Any such
separate firm for the Underwriters and such control persons of Underwriters
shall be designated in writing by Donaldson, Lufkin & Jenrette Securities
Corporation and any such separate firm for the Company, its directors, its
officers who sign the Registration Statement and such control persons of the
Company shall be designated in writing by the Company. No Indemnifying Person
shall be liable for any settlement of any proceeding effected without its
written consent, but if settled with such consent or if there be a final
judgment for the plaintiff, each Indemnifying Person agrees to indemnify any
Indemnified Person from and against any loss or liability by reason of such
settlement or judgment. Notwithstanding the foregoing sentence, if at any time
an Indemnified Person shall have requested an Indemnifying Person to reimburse
the Indemnified Person for fees and expenses of counsel as contemplated by the
second and third sentences of this paragraph, such Indemnifying Person agrees
that it shall be liable for any settlement of any proceeding effected without
its 

                                       29
<PAGE>
 
written consent if (i) such settlement is entered into more than 30 days
after receipt by such Indemnifying Person of the aforesaid request and (ii) such
Indemnifying Person shall not have reimbursed the Indemnified Person in
accordance with such request prior to the date of such settlement.  No
Indemnifying Person shall, without the prior written consent of the Indemnified
Person, effect any settlement of any pending or threatened proceeding in respect
of which any Indemnified Person is or could have been a party and indemnity
could have been sought hereunder by such Indemnified Person, unless such
settlement includes an unconditional release of such Indemnified Person from all
liability on claims that are the subject matter of such proceeding.

     If the indemnification provided for in this Section 7 is unavailable to an
Indemnified Person or insufficient in respect of any losses, claims, damages or
liabilities referred to therein, then each Indemnifying Person, in lieu of
indemnifying such Indemnified Person, shall contribute to the amount paid or
payable by such Indemnified Person as a result of such losses, claims, damages
or liabilities (i) in such proportion as is appropriate to reflect the relative
benefits received by the Company on the one hand and the Underwriters on the
other hand from the offering of the Shares or (ii) if the allocation provided by
clause (i) above is not permitted by applicable law, in such proportion as is
appropriate to reflect not only the relative benefits referred to in clause (i)
above but also the relative fault of the Company on the one hand and the
Underwriters on the other hand in connection with the statements or omissions
that resulted in such losses, claims, damages or liabilities, as well as any
other relevant equitable considerations. The relative benefits received by the
Company on the one hand and the Underwriters on the other hand shall be deemed
to be in the same respective proportions as the net proceeds from the offering
(before deducting expenses) received by the Company and the total underwriting
discounts and the commissions received by the Underwriters, in each case as set
forth in the table on the cover of the Prospectus, bear to the aggregate public
offering price of the Shares. The relative fault of the Company on the one hand
and the Underwriters on the other hand shall be determined by reference to,
among other things, whether the untrue or alleged untrue statement of a material
fact or the omission or alleged omission to state a material fact relates to
information supplied by the Company or by the Underwriters, and the parties'
relative intent, knowledge, access to information and opportunity to correct or
prevent such statement or omission.

     The Company and the Underwriters agree that it would not be just and
equitable if contribution pursuant to this Section 7 were determined by pro rata
allocation (even if the Underwriters were treated as one entity for such
purposes) or by any other method of allocation that does not take account of the
equitable considerations referred to in the immediately preceding paragraph. The
amount paid or payable by an Indemnified Person as a result of the losses,
claims, 

                                       30
<PAGE>
 
damages and liabilities referred to in the immediately preceding paragraph shall
be deemed to include, subject to the limitations set forth above, any legal or
other expenses incurred by such Indemnified Person in connection with
investigating or defending any such action or claim. Notwithstanding the
provisions of this Section 7, in no event shall an Underwriter be required to
contribute any amount in excess of the amount by which the total price at which
the Shares underwritten by it and distributed to the public were offered to the
public exceeds the amount of any damages that such Underwriter has otherwise
been required to pay by reason of such untrue or alleged untrue statement or
omission or alleged omission. No person guilty of fraudulent misrepresentation
(within the meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation. The Underwriters' obligations to contribute pursuant to this
Section 7 are several in proportion to the respective number of Shares set forth
opposite their names in Schedule I hereto, and not joint.

     The remedies provided for in this Section 7 are not exclusive and shall not
limit any rights or remedies which may otherwise be available to any indemnified
party at law or in equity.

     The indemnity and contribution agreements contained in this Section 7 and
the representations and warranties of the Company set forth in this Agreement
shall remain operative and in full force and effect regardless of (i) any
termination of this Agreement, (ii) any investigation made by or on behalf of
any Underwriter or any person controlling any Underwriter or by or on behalf of
the Company, its officers or directors or any other person controlling the
Company and (iii) acceptance of and payment for any of the Shares.

     8.   Notwithstanding anything herein contained, this Agreement (or the
obligations of the several Underwriters with respect to the Option Shares) may
be terminated in the absolute discretion of the Representatives, by notice given
to the Company, if after the execution and delivery of this Agreement and prior
to the Closing Date (or, in the case of the Option Shares, prior to the
Additional Closing Date) (i) trading generally shall have been suspended or
materially limited on or by, as the case may be, any of the New York Stock
Exchange, the American Stock Exchange or the NASD, (ii) trading of any
securities of or guaranteed by the Company shall have been suspended on any
exchange or in any over-the-counter market, (iii) a general moratorium on
commercial banking activities in New York shall have been declared by either
Federal or New York State authorities, or (iv) there shall have occurred any
outbreak or escalation of hostilities or any change in financial markets or any
calamity or crisis that, in the judgment of the Represen  tatives, is material
and adverse and which, in the judgment of the Representatives, makes it
impracticable to market the Shares being delivered at the Closing Date or 

                                       31
<PAGE>
 
the Additional Closing Date, as the case may be, on the terms and in the manner
contemplated in the Prospectus.

     9.   This Agreement shall become effective upon the later of (x) execution
and delivery hereof by the parties hereto and (y) release of notification of the
effectiveness of the Registration Statement (or, if applicable, any post-
effective amendment) by the Commission.

     If on the Closing Date or the Additional Closing Date, as the case may be,
any one or more of the Underwriters shall fail or refuse to purchase Shares
which it or they have agreed to purchase hereunder on such date, and the
aggregate number of Shares which such defaulting Underwriter or Underwriters
agreed but failed or refused to purchase is not more than one-tenth of the
aggregate number of Shares to be purchased on such date, the other Underwriters
shall be obligated severally in the proportions that the number of Shares set
forth opposite their respective names in Schedule I bears to the aggregate
number of Shares set forth opposite the names of all such non-defaulting
Underwriters, or in such other proportions as the Representatives may specify,
to purchase the Shares which such defaulting Underwriter or Underwriters agreed
but failed or refused to purchase on such date; provided that in no event shall
the number of Shares that any Underwriter has agreed to purchase pursuant to
Section 1 be increased pursuant to this Section 9 by an amount in excess of one-
tenth of such number of Shares without the written consent of such Underwriter.
If on the Closing Date or the Additional Closing Date, as the case may be, any
Underwriter or Underwriters shall fail or refuse to purchase Shares which it or
they have agreed to purchase hereunder on such date, and the aggregate number of
Shares with respect to which such default occurs is more than one-tenth of the
aggregate number of Shares to be purchased on such date, and arrangements
satisfactory to the Representatives and the Company for the purchase of such
Shares are not made within 36 hours after such default, this Agreement (or the
obligations of the several Underwriters to purchase the Option Shares, as the
case may be) shall terminate without liability on the part of any non-defaulting
Underwriter or the Company.  In any such case either you or the Company shall
have the right to postpone the Closing Date (or, in the case of the Option
Shares, the Additional Closing Date), but in no event for longer than seven
days, in order that the required changes, if any, in the Registration Statement
and in the Prospectus or in any other documents or arrangements may be effected.
Any action taken under this paragraph shall not relieve any defaulting
Underwriter from liability in respect of any default of such Underwriter under
this Agreement.

     10.  If this Agreement shall be terminated by the Underwriters, or any of
them, because of any failure or refusal on the part of the Company to comply
with the terms or to fulfill the conditions of this Agreement, or if for any
reason the Company shall be unable to perform its obligations under this
Agreement or any 

                                       32
<PAGE>
 
condition of the Underwriters' obligations cannot be fulfilled or is not waived,
the Company agrees to reimburse the Underwriters or such Underwriters as have so
terminated this Agreement with respect to themselves, severally, for all out-of-
pocket expenses (including the fees and expenses of its counsel) reasonably
incurred by the Underwriters in connection with this Agreement and the offering
contemplated hereunder. If the Agreement is terminated by the Company by reason
of the default of one or more of the Underwriters, the Company shall not be
obligated to reimburse any defaulting Underwriter on account of such expenses.

     11.  This Agreement shall inure to the benefit of and be binding upon the
Company, the Underwriters, each affiliate of any Underwriter which assists such
Underwriter in the distribution of the Shares, any controlling persons referred
to herein and their respective successors and assigns. Nothing expressed or
mentioned in this Agreement is intended or shall be construed to give any other
person, firm or corporation any legal or equitable right, remedy or claim under
or in respect of this Agreement or any provision herein contained. No purchaser
of Shares from any Underwriter shall be deemed to be a successor merely by
reason of such purchase.

     12.  Any action by the Underwriters or the Representatives hereunder may be
taken by the Representatives jointly or by Donaldson, Lufkin & Jenrette
Securities Corporation on behalf of the Underwriters or the Representatives, and
any such action taken by the Representatives jointly or by Donaldson, Lufkin &
Jenrette Securities Corporation shall be binding upon the Underwriters. All
notices and other communications hereunder shall be in writing and shall be
deemed to have been duly given if mailed or transmitted by any standard form of
telecommunication. Notices to the Underwriters shall be given to the
Representatives, c/o Donaldson, Lufkin & Jenrette Securities Corporation, 277
Park Avenue, New York, New York 10172; Attention:  Syndicate Department. Notices
to the Company shall be given to it at Lyondell Chemical Company, One Houston
Center, Suite 1600, 1221 McKinney Street, Houston, Texas (telefax:
(713) 652-4140); Attention: Robert J. Millstone, Esq.

     13.  This Agreement may be signed in counterparts, each of which shall be
an original and all of which together shall constitute one and the same
instrument.

     14.  THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH
THE LAWS OF THE STATE OF NEW YORK, WITHOUT GIVING EFFECT TO THE CONFLICTS OF
LAWS PROVISIONS THEREOF.

                                       33
<PAGE>
 
     15.  No amendment or waiver of any provision of this Agreement, nor consent
or approval to any departure therefrom, shall be effective unless given in
writing and signed by the parties hereto.

     If the foregoing is in accordance with your understanding, please sign and
return four counterparts hereof.

                                       34
<PAGE>
 
                                         Very truly yours,
          
                                         LYONDELL CHEMICAL COMPANY
          
          
                                         By: /s/ LYONDELL CHEMICAL COMPANY 
                                            __________________________________
<PAGE>
 
Accepted: May 11, 1999

DONALDSON, LUFKIN & JENRETTE      
  SECURITIES CORPORATION
J.P. MORGAN SECURITIES INC.
GOLDMAN, SACHS & CO.
MORGAN STANLEY & CO.  
  INCORPORATED
SALOMON SMITH BARNEY INC.
SCHRODER & CO. INC.

Acting severally on behalf of themselves 
  and the several Underwriters listed in
  Schedule I hereto.

By:  DONALDSON, LUFKIN & JENRETTE 
      SECURITIES CORPORATION



By: /s/ DONALDSON, LUFKIN & JENRETTE SECURITIES CORPORATION
    ________________________________________________________
<PAGE>
 
                                                                      SCHEDULE I


                                                         NUMBER OF SHARES
                     UNDERWRITER                         TO BE PURCHASED
                     -----------                         ----------------
Donaldson, Lufkin & Jenrette Securities Corporation.........    8,750,000
J.P. Morgan Securities Inc..................................    8,750,000
Goldman, Sachs & Co.........................................    3,937,500
Morgan Stanley & Co. Incorporated...........................    3,937,500
Salomon Smith Barney Inc....................................    3,937,500
Schroder & Co. Inc..........................................    3,937,500
ABN AMRO Incorporated.......................................      125,000
Banque Nationale de Paris...................................      125,000
Sanford C. Bernstein & Co., Inc.............................      125,000
BNY Capital Markets, Inc....................................      125,000
Chase Securities Inc........................................      125,000
CIBC World Markets Corp.....................................      125,000
Credit Lyonnais Securities (USA) Inc........................      125,000
Credit Suisse First Boston Corporation......................      125,000
Dresdner Kleinwort Benson North America LLC.................      125,000
NationsBanc Montgomery Securities LLC.......................      125,000
Neuberger & Berman..........................................      125,000
Scotia Capital Markets (USA) Inc............................      125,000
SG Cowen Securities Corporation.............................      125,000
TD Securities (USA) Inc.....................................      125,000

     Total..................................................   35,000,000
<PAGE>
 
                                                                       EXHIBIT A



                               LOCK-UP AGREEMENT


                                                   _________________, 1999



Donaldson, Lufkin & Jenrette
   Securities Corporation
J.P. Morgan Securities Inc.
Goldman, Sachs & Co.
Morgan Stanley & Co. Incorporated
Salomon Smith Barney Inc.
Schroder & Co. Inc.,
     As representatives of the several
     Underwriters listed in Schedule I
     to the Underwriting Agreement
c/o  Donaldson, Lufkin & Jenrette
        Securities Corporation
     277 Park Avenue
     New York, New York  10172

Re:  LYONDELL CHEMICAL COMPANY

Ladies and Gentlemen:

     The undersigned understands that you, as Representatives of the several
Underwriters, propose to enter into an Underwriting Agreement (the "UNDERWRITING
AGREEMENT") with Lyondell Chemical Company, a Delaware corporation (the
"COMPANY"), providing for the public offering (the "PUBLIC OFFERING") by the
several Underwriters named in Schedule I to the Underwriting Agreement (the
"UNDERWRITERS"), of ______ shares (the "SHARES") of common stock, par value
$1.00 per share, of the Company (the "COMMON STOCK").

     In consideration of the Underwriters' agreement to purchase and make the
Public Offering of the Shares, and for other good and valuable consideration,
receipt of which is hereby acknowledged, the undersigned hereby agrees that,
without the prior written consent of Donaldson, Lufkin & Jenrette Securities
Corporation on behalf of the Underwriters, the undersigned will not, during the
period ending 90 days after the date of the final prospectus relating to the
Public 


                                       1
<PAGE>
 
Offering (the "PROSPECTUS"), (1) offer, pledge, announce the intention to
sell, sell, contract to sell, sell any option or contract to purchase, purchase
any option or contract to sell, grant any option, right or warrant to purchase,
or otherwise transfer or dispose of, directly or indirectly, any shares of
Common Stock of the Company or any securities convertible into or exercisable or
exchangeable for Common Stock (including without limitation, Common Stock which
may be deemed to be beneficially owned by the undersigned in accordance with the
rules and regulations of the Securities and Exchange Commission and securities
which may be issued upon exercise of a stock option or warrant) or (2) enter
into any swap or other agreement that transfers, in whole or in part, any of the
economic consequences of ownership of the Common Stock, whether any such
transaction described in clause (1) or (2) above is to be settled by delivery of
Common Stock or such other securities, in cash or otherwise.  In addition, the
undersigned agrees that, without the prior written consent of Donaldson, Lufkin
& Jenrette Securities Corporation on behalf of the Underwriters, it will not,
during the period ending 90 days after the date of the Prospectus, make any
demand for or exercise any right with respect to the registration of any shares
of Common Stock or any security convertible into or exercisable or exchangeable
for Common Stock.

     In furtherance of the foregoing, the Company, and any duly appointed
transfer agent for the registration or transfer of the securities described
herein, are hereby authorized to decline to make any transfer of securities if
such transfer would constitute a violation or breach of this lock-up agreement.

     The undersigned hereby represents and warrants that the undersigned has
full power and authority to enter into this lock-up agreement.  All authority
herein conferred or agreed to be conferred and any obligations of the
undersigned shall be binding upon the successors, assigns, heirs or personal
representatives of the undersigned.

     The undersigned understands that if the Underwriting Agreement does not
become effective, or if the Underwriting Agreement (other than the provisions
thereof which survive termination) shall terminate or be terminated prior to
payment for and delivery of the Common Stock to be sold thereunder, the
undersigned shall be released from all obligations under this lock-up agreement.

     The undersigned understands that the Underwriters are entering into the
Underwriting Agreement and proceeding with the Public Offering in reliance upon
this lock-up agreement.

                                       2
<PAGE>
 
     This lock-up agreement shall be governed by and construed in accordance
with the laws of the State of New York, without giving effect to the conflicts
of laws provisions thereof.

                                         Very truly yours,
        
                                         [NAME OF STOCKHOLDER]
        
        
        
                                         By: _______________________________
                                             Name:
                                             Title:

Accepted as of the date first set forth 
   above:

DONALDSON, LUFKIN & JENRETTE          
   SECURITIES CORPORATION
J.P. MORGAN SECURITIES INC.
GOLDMAN, SACHS & CO.
MORGAN STANLEY & CO.    
   INCORPORATED
SALOMON SMITH BARNEY INC.
SCHRODER & CO. INC.
Acting severally on behalf of themselves 
   and the several Underwriters named in
   Schedule I to the Underwriting 
   Agreement


By: DONALDSON, LUFKIN & 
    JENRETTE SECURITIES 
    CORPORATION


By: ________________________________
    Name:
    Title:


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