<PAGE>

                                                                    EXHIBIT 10.2

                 FIRST AMENDMENT TO INDEMNIFICATION AGREEMENT
                 --------------------------------------------

     This First Amendment to Indemnification Agreement (the "Amendment
Agreement") is dated as of December 31, 1997, and is between TCI Satellite
Entertainment, Inc., a Delaware corporation (the "Company") and TCI UA 1, Inc.,
a Colorado corporation ("Account Party").

     RECITALS:

     A.   The Company and the Account Party executed and delivered an
Indemnification Agreement, dated as of December 4, 1996 (the "Indemnification
Agreement"), wherein the Company agreed (i) to reimburse the Account Party for
payments made pursuant to an Irrevocable Transferable Letter of Credit No. T-
253097 ("Letter of Credit"), and (ii) to indemnify the Account Party for any
losses incurred related to the Letter of Credit and an Amended and Restated
Reimbursement Agreement dated as of March 1, 1995, among the Account Party,
Chemical Bank and The Toronto Dominion Bank.

     B.   The parties desire to extend the expiry date of the Letter of Credit
to June 30, 1999.

     C.   The Account Party and the Company desire to amend the Indemnification
Agreement to provide for certain additional terms related to any reimbursement
or indemnification of any payments made pursuant to the Letter of Credit.

     NOW THEREFORE, in consideration of the premises and other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, the
parties hereby agree as follows:

     Paragraph A.  Amendment to Section 1.
                   ----------------------

     Section 1 of the Indemnification Agreement is hereby amended to add the
following paragraph:

          (d)

                (i)   In addition to the Payment Amounts due hereunder, the
          Company shall pay to Account Party, as a facility fee, 1/8th of 1% of
          the available amount drawable under the Letter of Credit on the date
          of the Amendment Agreement. The Company shall pay such facility fee
          upon the execution of the Amendment Agreement. In addition, the
          Account Party agrees to extend the expiry date of the Letter of Credit
          to June 30, 1999 when the Letter of Credit next expires after the date
          hereof.

                (ii)  In addition to the Payment Amounts due hereunder, the
          Company shall pay to the Account Party monthly, in advance, a letter
          of credit fee of 1/10/th/ of
<PAGE>





          1% per annum of the available amounts drawable under the Letter of
          Credit, until the Letter of Credit expires. Such payment shall be due
          on the first of each month, beginning January 1, 1998.

     Paragraph B.  Miscellaneous.
                   -------------

          (a)      This Amendment Agreement may be executed in one or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

          (b)      The section headings contained in this Amendment Agreement
are inserted for reference purposes only and shall not affect the meaning of
interpretation of this Amendment Agreement.

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment Agreement
to be executed as of the day and year first above written.

                                        TCI UA 1, INC.



                                        By:______________________________
                                           Name:
                                           Title:




                                        TCI SATELLITE ENTERTAINMENT, INC.


                                        BY:______________________________
                                           Name:
                                           Title:

                                      -2-