Chapman and Cutler LLP
                             111 West Monroe Street
                             Chicago, Illinois 60603


                               September 25, 2013


Securities and Exchange Commission
100 F Street NE
Washington, D.C.  20549


                 Re: Guggenheim Defined Portfolios, Series 1040
                Zacks Indicator Defined Outcome Trust, Series 1
                              File No. 333-188046
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Ladies and Gentlemen:

      On behalf of Guggenheim Funds Distributors, LLC, depositor, sponsor and
underwriter of the Guggenheim Defined Portfolios, Series 1040, consisting of the
above-captioned trust (the "Trust"), there is enclosed Amendment No. 2 to the
Registration Statement on Form S-6 relating to securities of Guggenheim Defined
Portfolios, Series 1040 (the "Fund").

      The Reference Trust Agreement was entered into by Guggenheim Funds
Distributors, LLC, as Depositor, and The Bank of New York Mellon, as Trustee, on
the date hereof, and Securities (or delivery statements relating to contracts
for the purchase thereof) in the aggregate amount of the portfolio(s) have been
deposited with the Trustee. In connection therewith the Trustee is prepared to
establish book entry positions which are being retained by the Trustee for
delivery after the effectiveness of the Registration Statement.

      In addition to Amendment No. 2, the exhibits listed therein are submitted
herewith.

      Except as indicated in the Memorandum of Changes, the changes in the
Prospectus represent primarily responses to the staff of the Securities &
Exchange Commission's comments, the completion of various statements regarding
the Securities deposited in the Trust and the dates of record, deposit,
distribution, termination and evaluation, together with a list of the Securities
which will comprise the portfolio of the Trust, the Statement of Financial
Condition of the Trust and the Report of Independent Registered Public
Accounting Firm.

      We have appreciated the courtesy and cooperation of the members of the
Staff and if there are any questions on which we may be of assistance, please do
not hesitate to call either Eric F. Fess (312-845-3781) or Morrison C. Warren
(312-845-3484) collect.

                                                               Very truly yours,


                                                      /s/ Chapman and Cutler LLP
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                                                          CHAPMAN AND CUTLER LLP