NUVEEN TAX FREE UNIT TRUST SERIES 1038, 497J, 1998-11-03

NUVEEN TAX FREE UNIT TRUST SERIES 1038
497J, 1998-11-03

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                                                                NOVEMBER 3, 1998
 
(ON CHAPMAN AND CUTLER LETTERHEAD)
 
SECURITIES AND EXCHANGE COMMISSION
450 FIFTH STREET, N.W.
WASHINGTON, D.C. 20549
 
RE:  Nuveen Unit Trust, Series 1038
 
     File No. 333-66037
 
     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 most recent
     amendment to the Registration Statement on Form S-6 (the "Registration
     Statement") of the above-referenced Series does not differ from that which
     would have been filed pursuant to Rule 487(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 3,
     1998.
 
     Very truly yours,
 
     Chapman and Cutler