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                                                                   EXHIBIT 10.34


                          OPTION TO PURCHASE AGREEMENT


         This OPTION TO PURCHASE AGREEMENT (this "Agreement") is made this 16th
day of December 1998, by and among PIONEER NATURAL RESOURCES USA, INC., a
Delaware corporation ("Pioneer USA"), PIONEER RESOURCES PRODUCING L.P., a
Delaware limited partnership ("Pioneer Producing" and collectively with Pioneer
USA, "Seller"), and COSTILLA ENERGY, INC., a Delaware corporation ("Purchaser").

                                  WITNESSETH:

         1. Grant of Option. For the consideration provided below in Section 2,
Seller hereby grants to Purchaser, for the period commencing immediately after
receipt by Seller of evidence reasonably satisfactory to Seller that Purchaser
has provided its stock transfer agent with irrevocable instructions to issue to
Pioneer the stock certificate described below in Section 2(a), and ending at
9:00 a.m. on March 17, 1999 (the "Option Period"), the sole, exclusive and
irrevocable right and option (the "Option"), but not the obligation, to purchase
and acquire the Assets from Seller on the Closing Date at and for the
consideration and upon the terms contained in that certain Purchase and Sale
Agreement in the form attached hereto as Appendix A (the "Purchase Agreement"),
the terms, provisions and exhibits of which are incorporated herein for all
purposes, including, without limitation, (a) the definitions of undefined,
capitalized terms used in this Agreement, and (b) a description of the Assets.

         2. Option Consideration. Purchaser and Pioneer USA were parties to that
certain Purchase and Sale Agreement dated September 4, 1998 (the "Prior
Agreement"). Pursuant to the terms of the Prior Agreement, Purchaser made a
deposit (the "Deposit") in the amount of $25,000,000 by wire transfer to Pioneer
USA. This Agreement is being executed to replace and supersede the Prior
Agreement, which Prior Agreement is being terminated as a part of this Agreement
and is hereby no longer of any force or effect. Seller acknowledges and agrees
that said $25,000,000 is in its possession, and Purchaser and Seller acknowledge
and agree that Seller's possession of said $25,000,000 is partial consideration
for the Option and this Agreement. All rights of Purchaser relating in any way
to the Deposit under the Prior Agreement are hereby forever extinguished.
Further, as additional consideration, Purchaser (a) shall deliver to Pioneer
USA, on or before December 23, 1998, a stock certificate representing 3,000,000
shares of the common stock, par value $.10 per share, of Purchaser (the
"Shares") duly endorsed and registered in the name of Pioneer USA, and (b)
hereby disclaims any right, title or interest in or to the property described in
Appendix B attached hereto (the "Sonat Interest"), and hereby sells, assigns and
transfers to Pioneer USA all of Purchaser's right, title and interest (if any)
in and to the Sonat Interest. The Sonat Interest is the subject of that certain
letter agreement dated October 9, 1998, by and between Pioneer USA and Purchaser
(the "Sonat Letter Agreement"), a copy of which is attached hereto as Appendix
C. By executing and entering into this Agreement, Purchaser and Seller
acknowledge and agree that the Sonat Letter Agreement is hereby terminated and
is no longer of any force or effect. From and after the date of this Agreement,
Purchaser agrees to perform all acts and do all things (including, without
limitation, executing appropriate assignments) reasonably requested by Seller in
order to more fully and effectively convey the Sonat Interest to Pioneer USA as
contemplated by subsection (b) above.


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         The consideration described above shall hereinafter be referred to as
the "Option Consideration". The Option Consideration is not a deposit and is not
in any event (including, without limitation, the expiration or termination of
the Option, this Agreement or the Purchase Agreement) refundable.

         3. Exercise of the Option. In order to exercise the Option, Purchaser
must (a) notify Seller in writing before the expiration of the Option Period
that Purchaser desires to purchase from Seller the Assets in accordance with the
terms and provisions set forth in the Purchase Agreement, (b) deliver to Seller
the evidence of Purchaser's instructions to its transfer agent as contemplated
by and in accordance with Section 1 above, and (c) deliver to Seller two (2)
copies of the Purchase Agreement (in the form of the attached Appendix A) duly
executed by Purchaser. Upon full compliance by Purchaser with the foregoing
provisions of this Section 3, Seller shall promptly counter-execute both such
copies of the Purchase Agreement and return one fully-executed copy of the
Purchase Agreement to Seller, whereupon Seller and Purchaser shall have entered
into the Purchase Agreement.

         4. Expiration of the Option and Termination of this Agreement. The
Option shall expire and this Agreement shall terminate immediately upon the
happening of any of the following events: (a) Purchaser validly exercises the
Option and Purchaser and Seller execute and enter into the Purchase Agreement;
(b) Purchaser fails to deliver to Pioneer USA the stock certificate described
above in Section 2(a) on or before December 23, 1998; or (c) Purchaser fails to
validly exercise the Option by 9:00 a.m. on March 17, 1999. Upon the expiration
of the Option and the termination of this Agreement, neither Purchaser nor
Seller shall have any further rights, duties or obligations hereunder, except
for Purchaser's duties and obligations (and Seller's rights) under Section 2
above (including, without limitation, Purchaser's duty to deliver to Seller the
stock certificate representing the Shares), which shall survive any expiration
or termination of the Option, this Agreement or the Purchase Agreement.

         5. Governing Law. This Agreement and the transactions contemplated
hereby shall be construed in accordance with, and governed by, the laws of the
State of Texas.

         EXECUTED as of the date first set forth above.

                         PIONEER USA:

                         PIONEER NATURAL RESOURCES USA, INC.

                         By: /s/ MARK L. WITHROW
                             ---------------------------------------------------
                         Name:   Mark L. Withrow
                         Title:  Executive Vice President & General Counsel

                         PIONEER PRODUCING:

                         PIONEER RESOURCES PRODUCING L.P.

                           By:   Pioneer Resources, Inc., its General Partner

                                 By: /s/ MARK L. WITHROW
                                     -------------------------------------------
                                 Name:   Mark L. Withrow
                                 Title:  Executive Vice President


                         PURCHASER:

                         COSTILLA ENERGY, INC.

                         By: /s/ CLIFFORD N. HAIR, JR.
                             ---------------------------------------------------
                         Name:   Clifford N. Hair, Jr.
                         Title:  Senior Vice President -- Land



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