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


                               September 18, 2017


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


                 Re: Guggenheim Defined Portfolios, Series 1664
                   European High Dividend Portfolio, Series 9
                       File Nos. 333-219894 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 1664, filed on August 11, 2017, with
the Securities and Exchange Commission (the "Commission"). The registration
statement proposes to offer the European High Dividend Portfolio, Series 9 (the
"Trust").

PROSPECTUS

Investment Summary -- Security Selection

     1. In Item No. 3, please state the market capitalization range for small
capitalization companies according to the Russell Global Index Methodology.

     Response: The registration statement has been revised in accordance with
this comment.

Investment Summary -- Hypothetical Performance Information

     2. In the Hypothetical Comparison of Total Return, please delete data
related to the years 2000-2006.

     Response: The sponsor has standardized its hypothetical performance
disclosure across its unit investment trusts to show the performance of the
trusts from 2000 to the present year whenever such information is available. The
sponsor believes this allows investors to compare the performance across trusts
using the same time periods and provides them with information for a multitude
of economic cycles. As a result, the sponsor respectfully declines to revise the
prospectus to remove the data related to years 2000-2006.

     3. Please identify the party who calculated the hypothetical performance
data.

     Response: The registration statement has been revised in accordance with
this comment.

     4. Please confirm the following:

     a. The Trust maintains the books and records of the information that
substantiates the back-tested performance.

     b. The Trust has adopted policies and procedures as required by Rule 38a-1
under the Investment Company Act of 1940 (the "Act") designed to prevent the
Trust from violating Section 34(b) of the Act when the Trust discloses
back-tested performance.

     Response: The sponsor confirms that it: (a) maintains the books and records
of the information that substantiates the back-tested performance; and (b) has
adopted policies and procedures as required by Rule 38a-1 under the Act designed
to prevent the Trust from violating Section 34(b) of the Act when the Trust
discloses back-tested performance.

     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