<PAGE>
 
                                                                   EXHIBIT 10.13



                                    October 31, 1996



Cheniere Energy Operating Company, Inc.
237 Park Avenue, Suite 2100
New York, NY  10017


                                                  RE:  Third Amendment

Gentlemen:

     I am writing with respect to that certain Exploration Agreement dated April
4, 1996, by and between FX Energy, Inc., and Zydeco Exploration, Inc., as
amended by that certain First Amendment dated May 15, 1996, and that certain
Second Amendment dated August 5,1996 (the Agreement).  For convenience, terms
defined therein shall have the same meaning when used herein.  FX Energy, Inc.
(FX) has changed its name to Cheniere Energy Operating Co., Inc. (Cheniere).

     Section 2 of the Agreement originally provided:

       FX shall pay the Seismic Funds to ZEI for deposit in the segregated
     account described in Section 12.a on the following schedule.

<TABLE>                    
<CAPTION>                  
                         DATE             AMOUNT    
                         ------------  -------------
                         <S>           <C>          
                                                    
                         1996-05-15    $3,000,000.00
                                                    
                         1996-06-30     1,000,000.00
                                                    
                         1996-07-30     1,000,000.00
                                                    
                         1996-08-30     1,000,000.00
                                                    
                         1996-09-30     2,000,000.00
                                                    
                         1996-10-30     1,000,000.00
                                                    
                         1996-11-30     1,000,000.00
                                                    
                         1996-12-30     1,000,000.00
                                                    
                         1997-01-30     1,000,000.00
                                                    
                         1997-02-28     1,500,000.00 
</TABLE>


<PAGE>

 
Cheniere Energy Operating Company, Inc.
October 31, 1996
Page 2


          Through yesterday, October 30, 1996, Cheniere had paid $5,000,000.00.
We wish to provide an alternate schedule for the remaining payments, which is:

<TABLE>
<CAPTION>
                         DATE             AMOUNT      
                         ----             ------     
                         <S>           <C>           
                                                     
                         1996-10-31    $1,000,000.00 
                                                     
                         1996-11-30     2,000,000.00 
                                                     
                         1997-01-31     2,000,000.00 
                                                     
                         1997-02-28     2,000,000.00 
                                                     
                         1997-03-31     1,500,000.00  
</TABLE>

     Further:

     1.   Should Cheniere fail to make the payment of $2,000,000.00 due November
          30, 1996, by such date, such failure shall be treated as a
          Discontinuance under Section 5.

     2.   As to the payments due January 31, 1997, February 28, 1997, and March
          31, 1997, the normal grace period shall apply.

     3.   The parties agree that the agreements by Zydeco to defer payments
          under Section 2 do not obligate Zydeco to grant further waivers nor
          waive the rights of Zydeco to have payments made at the times provided
          in the Agreement, as modified hereby.

     If I have correctly set forth our agreements, kindly so indicate by
executing one counterpart of this letter and returning it to the undersigned.

                                                  Yours very truly,

                                                  ZYDECO EXPLORATION, INC.
 
 
                                                  /s/ W. Kyle Willis
                                                  ------------------------------
                                                  W. Kyle Willis
                                                  Vice President


ACCEPTED AND AGREED TO THIS
31ST DAY OF OCTOBER, 1996.

CHENIERE ENERGY OPERATING COMPANY, INC.


/s/ William D. Forster
---------------------------------------
President