NUVEEN TAX FREE UNIT TRUST SERIES 1043, 497J, 1998-11-19

NUVEEN TAX FREE UNIT TRUST SERIES 1043
497J, 1998-11-19

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                                                               NOVEMBER 19, 1998
 
(ON CHAPMAN AND CUTLER LETTERHEAD)
 
SECURITIES AND EXCHANGE COMMISSION
450 FIFTH STREET, N.W.
WASHINGTON, D.C. 20549
 
RE:  Nuveen Unit Trust, Series 1043
 
     File No. 333-67237
 
     Dear Sir or Madam:
 
   
     On behalf of John Nuveen & Co. Incorporated, in accordance with the
     provisions of Rule 497(j) of Regulation C under the Securities Act of 1933
     (the "Securities Act"), this letter serves to certify that the form of
     Prospectus and Information Supplement contained in the most recent
     amendment to the Registration Statement on Form S-6 (the "Registration
     Statement") of the above-referenced Series do not differ from that which
     would have been filed pursuant to Rule 497(b) of the Securities Act.
     Amendment No. 1, which was the most recent amendment to the Registration
     Statement, was filed electronically with the Commission on November 19,
     1998.
    
 
     Very truly yours,
 
     Chapman and Cutler