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


                                December 3, 2014


Mr. Edward Bartz
Division of Investment Management
Securities and Exchange Commission
100 F Street, N.E.
Washington, DC  20549


                 Re: Guggenheim Defined Portfolios, Series 1257
                     MLP & Energy Funds Portfolio, Series 8
                       File Nos. 333-199543 and 811-03763
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Dear Mr. Bartz:

      This letter is in response to your comments given during a telephone
conversation with our office regarding the registration statement on Form S-6
for Guggenheim Defined Portfolios, Series 1257, filed on October 22, 2014 with
the Securities and Exchange Commission (the "Commission"). The registration
statement offers the MLP & Energy Funds Portfolio, Series 8 (the "trust").

PROSPECTUS

Investment Summary -- Principal Risks

     1. The "Principal Investment Strategy" section states that the trust may
invest in foreign companies. Please add disclosure about the risks of investing
in foreign companies in the "Principal Risks" section.

     Response: Even though foreign company securities may be included in the
portfolio, we include risks based upon the final portfolio. If such securities
are selected for the portfolio of this trust, we will add the appropriate risk
disclosures.

     2. The "Principal Investment Strategy" section states that the trust may
invest in companies headquartered or incorporated in countries considered to be
emerging markets. Please add disclosure about the risks of investing in emerging
markets in the "Principal Risks" section.

     Response: Even though securities of companies headquartered or incorporated
in countries considered to be emerging markets may be included in the portfolio,
we include risks based upon the final portfolio. If such securities are selected
for the portfolio of this trust, we will add the appropriate risk disclosures.

     We appreciate your prompt attention to this registration statement. If you
have any questions or comments or would like to discuss our responses to your
questions please feel free to contact the undersigned at (312) 845-3484.

                                                               Very truly yours,

                                                          CHAPMAN AND CUTLER LLP


                                                       By /s/ Morrison C. Warren
                                                       -------------------------
                                                              Morrison C. Warren