<PAGE>
                                                                     Exhibit 4.4

                       AMENDMENT NO. 1 TO RIGHTS AGREEMENT

     Amendment No. 1, dated as of January 31, 2006, to the Rights Agreement
dated as of January 31, 1996 (the "Agreement"), between Apache Corporation, a
Delaware corporation (the "Company"), and Wells Fargo Bank, N.A. (successor to
Norwest Bank Minnesota, N.A., the "Rights Agent").

     The Company has approved the amendment to the Agreement set forth below.
Accordingly, in consideration of the premises and mutual agreements herein set
forth, the parties hereby agree as follows:

     FIRST: The first paragraph of Section 7 of the Agreement is hereby amended
to read in its entirety as follows:

     "(a) Except as otherwise provided herein, the Rights shall become
exercisable on the Distribution Date, and thereafter the registered holder of
any Right Certificate may, subject to Section 11(a)(ii) hereof and except as
otherwise provided herein, exercise the Rights evidenced thereby in whole or in
part upon surrender of the Right Certificate, with the form of election to
purchase on the reverse side thereof duly executed, to the Rights Agent at the
office or agency of the Rights Agent designated for such purpose, together with
payment of the aggregate Purchase Price with respect to the total number of one
ten-thousandths of a share of Preferred Stock (or other securities, cash or
other assets, as the case may be) as to which the Rights are exercised, at any
time which is both after the Distribution Date and prior to the time (the
"Expiration Date") that is the earliest of (i) the Close of Business on January
31, 2016 (the "Final Expiration Date"), (ii) the time at which the Rights are
redeemed as provided in Section 23 hereof (the "Redemption Date") or (iii) the
time at which such Rights are exchanged as provided in Section 24 hereof."

     SECOND: Section 11(m) of the Agreement is hereby amended to read in its
entirety as follows:

     "Effective as of January 31, 2006, each 0.4329 Rights associated with each
share of Common Stock is reclassified into one whole Right, such that,
notwithstanding the provisions of Section 11(m) of this Agreement as applied
prior to such date, as of and from such date, until subsequently adjusted in
accordance with the provisions hereof, each share of Common Stock has associated
with it one whole Right."

     THIRD: The form of Right Certificate attached to the Agreement as Exhibit B
shall be replaced in its entirety by the form of the Right Certificate attached
hereto.

     FOURTH: This Amendment shall be effective as of the date hereof.

     FIFTH: Except as set forth above, the provisions of the Agreement shall
remain in full force and effect.

<PAGE>

     SIXTH: This Amendment shall be deemed to be a contract made under the laws
of the State of Delaware and for all purposes shall be governed by and construed
in accordance with the laws of such state applicable to contracts to be made and
performed entirely within such state. This Amendment may be executed in any
number of counterparts, each of such counterparts shall for all purposes be
deemed to be an original, and all such counterparts shall together constitute
but one and the same instrument. If any term, provision, covenant or restriction
of this Amendment is held by a court of competent jurisdiction or other
authority to be invalid, illegal, or unenforceable, the remainder of the terms,
provisions, covenants and restrictions of this Amendment shall remain in full
force and effect and shall in no way be affected, implied or invalidated.

     IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed prior to the close of business on January 31, 2006.

                                        APACHE CORPORATION


                                        By: /s/ Roger B. Plank
                                            ------------------------------------
                                        Name: Roger B. Plank
                                        Title: Executive Vice President and
                                               Chief Financial Officer


                                        WELLS FARGO BANK, N.A.


                                        By: /s/ Barbara M. Novak
                                            ------------------------------------
                                        Name: Barbara M. Novak
                                        Title: Vice President

<PAGE>

                                                                       EXHIBIT B

                            Form of Right Certificate

Certificate No. R- ____

     NOT EXERCISABLE AFTER JANUARY 31, 2016 OR EARLIER IF REDEMPTION OR EXCHANGE
     OCCURS. THE RIGHTS ARE SUBJECT TO REDEMPTION AT $.01 PER RIGHT AND TO
     EXCHANGE ON THE TERMS SET FORTH IN THE RIGHTS AGREEMENT. UNDER CERTAIN
     CIRCUMSTANCES, AS SET FORTH IN THE RIGHTS AGREEMENT, RIGHTS OWNED BY OR
     TRANSFERRED TO ANY PERSON WHO IS OR BECOMES AN ACQUIRING PERSON (AS DEFINED
     IN THE RIGHTS AGREEMENT) AND CERTAIN TRANSFEREES THEREOF WILL BECOME NULL
     AND VOID AND WILL NO LONGER BE TRANSFERABLE.

                                Right Certificate

                               APACHE CORPORATION

     This certifies that _______________ or registered assigns, is the
registered owner of the number of Rights set forth above, each of which entitles
the owner thereof, subject to the terms, provisions and conditions of the Rights
Agreement, dated as of January 31, 1996, as the same may be amended from time to
time (the "Rights Agreement"), between Apache Corporation, a Delaware
corporation (the "Company"), and Wells Fargo Bank, N.A. (formerly Norwest Bank
Minnesota, N.A.), as Rights Agent (the "Rights Agent"), to purchase from the
Company at any time after the Distribution Date (as such term is defined in the
Rights Agreement) and prior to 5:00 P.M., Houston, Texas time, on January 31,
2016 at the office or agency of the Rights Agent designated for such purpose, or
of its successor as Rights Agent, one ten-thousandth of a fully paid
non-assessable share of Series A Junior Participating Preferred Stock, no par
value per share (the "Preferred Stock"), of the Company, at a purchase price of
$100 per one ten-thousandth of a share of Preferred Stock (the "Purchase
Price"), upon presentation and surrender of this Right Certificate with the Form
of Election to Purchase duly executed. The number of Rights evidenced by this
Rights Certificate (and the number of one ten-thousandths of a share of
Preferred Stock which may be purchased upon exercise hereof) set forth above,
and the Purchase Price set forth above, are the number and Purchase Price as of
January 31, 1996, based on the Preferred Stock as constituted at such date. As
provided in the Rights Agreement, the Purchase Price, the number of one
ten-thousandths of a share of Preferred Stock (or other securities or property)
which may be purchased upon the exercise of the Rights and the number of Rights
evidenced by this Right Certificate are subject to modification and adjustment
upon the occurrence of certain events.


                                       B-1

<PAGE>

     This Right Certificate is subject to all of the terms, provisions and
conditions of the Rights Agreement, which are hereby incorporated herein by
reference and made a part hereof and to which Rights Agreement reference is
hereby made for a full description of the rights, limitations of rights,
obligations, duties and immunities hereunder of the Rights Agent, the Company
and the holders of the Right Certificates. Copies of the Rights Agreement are on
file at the principal executive offices of the Company and the above-mentioned
office or agency of the Rights Agent. The Company will mail to the holder of
this Right Certificate a copy of the Rights Agreement without charge after
receipt of a written request therefor.

     This Right Certificate, with or without other Right Certificates, upon
surrender at the office or agency of the Rights Agent designated for such
purpose, may be exchanged for another Right Certificate or Right Certificates of
like tenor and date evidencing Rights entitling the holder to purchase a like
aggregate number of shares of Preferred Stock as the Rights evidenced by the
Right Certificate or Right Certificates surrendered shall have entitled such
holder to purchase. If this Right Certificate shall be exercised in part, the
holder shall be entitled to receive upon surrender hereof another Right
Certificate or Right Certificates for the number of whole Rights not exercised.

     No fractional shares of Preferred Stock will be issued upon the exercise of
any Right or Rights evidenced hereby (other than fractions which are integral
multiples of one ten-thousandth of a share of Preferred Stock, which may, at the
election of the Company, be evidenced by depositary receipts), but in lieu
thereof a cash payment will be made, as provided in the Rights Agreement.

     Subject to the provisions of the Rights Agreement, the Rights evidenced by
this Certificate (i) may be redeemed by the Company at a redemption price of
$.01 per Right or (ii) may be exchanged in whole or in part for shares of the
Company's Common Stock, par value $0.625 per share, or shares of Preferred
Stock.

     No holder of this Right Certificate, as such, shall be entitled to vote or
receive dividends or be deemed to be for any purpose, the holder of the
Preferred Stock or of any other securities of the Company which may at any time
be issuable on the exercise hereof, nor shall anything contained in the Rights
Agreement or herein be construed to confer upon the holder hereof, as such, any
of the rights of a stockholder of the Company or any right to vote for the
election of directors or upon any matter submitted to stockholders at any
meeting thereof, or to give or withhold consent to any corporate action, or to
receive notice of meetings or other actions affecting stockholders (except as
provided in the Rights Agreement) or to receive dividends or subscription
rights, or otherwise, until the Right or Rights evidenced by this Right
Certificate shall have been exercised as provided in the Rights Agreement.

     This Right Certificate shall not be valid or obligatory for any purpose
until it shall have been countersigned by the Rights Agent.


                                       B-2

<PAGE>

     WITNESS the facsimile signature of the proper officers of the Company and
its corporate seal. Dated ________________ __, 20___.

                                        APACHE CORPORATION


ATTEST:                                 By:
                                            ------------------------------------
                                            [Title]

-------------------------------------
[Title]

Countersigned:

WELLS FARGO BANK, N.A.
as Rights Agent


By:
    ---------------------------------
    [Title]


                                       B-3

<PAGE>

                    Form of Reverse Side of Right Certificate

                               FORM OF ASSIGNMENT

                (To be executed by the registered holder if such
                holder desires to transfer the Right Certificate)

     FOR VALUE RECEIVED ___________________________ hereby sells, assigns and
transfers unto ___________________________________________________________
               (Please insert social security or other identifying number)

________________________________________________________________________
                  (Please print name and address of transferee)

________________________________________________________________________
Rights represented by this Right Certificate, together with all right, title and
interest therein, and does hereby irrevocably constitute and appoint
________________________ Attorney, to transfer said Rights on the books of the
within-named Company, with full power of substitution.

Dated:
       -----------


                                        ----------------------------------------
                                        Signature

Signature Guarantee:

     Signatures must be guaranteed by a bank, trust company, broker, dealer or
other eligible institution participating in a recognized signature guarantee
medallion program.

________________________________________________________________________
                                (To be completed)

     The undersigned hereby certifies that the Rights evidenced by this Right
Certificate are not beneficially owned by, were not acquired by the undersigned
from, and are not being assigned to an Acquiring Person or an Affiliate or
Associate thereof (as defined in the Rights Agreement).


                                        ----------------------------------------
                                        Signature


                                       B-4

<PAGE>

              Form of Reverse Side of Right Certificate - continued

                          FORM OF ELECTION TO PURCHASE

                  (To be executed if holder desires to exercise
                  Rights represented by the Rights Certificate)

To APACHE CORPORATION:

     The undersigned hereby irrevocably elects to exercise ___________ Rights
represented by this Right Certificate to purchase the shares of Preferred Stock
(or other securities or property) issuable upon the exercise of such Rights and
requests that certificates for such shares of Preferred Stock (or such other
securities) be issued in the name of:

________________________________________________________________________
                         (Please print name and address)

________________________________________________________________________

If such number of Rights shall not be all the Rights evidenced by this Right
Certificate, a new Right Certificate for the balance remaining of such Rights
shall be registered in the name of and delivered to:

Please insert social security
or other identifying number _______________________________

________________________________________________________________________
                         (Please print name and address)

________________________________________________________________________

Dated:
       ----------------


                                        ----------------------------------------
                                        Signature

        (Signature must conform to holder specified on Right Certificate)

Signature Guarantee:

Signatures must be guaranteed by a bank, trust company, broker, dealer or other
eligible institution participating in a recognized signature guarantee medallion
program.


                                       B-5

<PAGE>

              Form of Reverse Side of Right Certificate - continued

    ________________________________________________________________________
                                (To be completed)

     The undersigned certifies that the Rights evidenced by this Right
Certificate are not beneficially owned by, and were not acquired by the
undersigned from, an Acquiring Person or an Affiliate or Associate thereof (as
defined in the Rights Agreement).


                                        ----------------------------------------
                                        Signature

                                     NOTICE

     The signature on the Form of Assignment or Form of Election to Purchase, as
the case may be, must conform to the name as written upon the face of this Right
Certificate in every particular, without alteration, enlargement or any change
whatsoever.

     In the event the certification set forth above in the Form of Assignment or
the Form of Election to Purchase, as the case may be, is not completed, such
Assignment or Election to Purchase will not be honored.


                                       B-6