Exhibit   4.1



                       FIRST AMENDMENT TO RIGHTS AGREEMENT


                  THIS  AMENDMENT  (this  "Amendment"),  dated as of October 14,
1998,  to  the  Rights  Agreement,  dated  as  of  July  9,  1996  (the  "Rights
Agreement"),  by and between Kerr-McGee Corporation, a Delaware corporation (the
"Company"),  and Bank One Trust  Company,  N.A.*,  as Rights  Agent (the "Rights
Agent").

                                 R E C I T A L S

     WHEREAS,  the Company and the Rights  Agent have  heretofore  executed  and
entered into the Rights Agreement;

     WHEREAS,  pursuant to Section 27 of the Rights  Agreement,  the Company may
from time to time  supplement or amend the Rights  Agreement in accordance  with
the provisions thereof;

     WHEREAS,  the Company  intends to enter into (i) an  Agreement  and Plan of
Merger, dated as of October 14, 1998 (as it may be further amended, supplemented
or otherwise  modified from time to time, the "Merger  Agreement")  between Oryx
Energy Company  ("Oryx") and the Company,  pursuant to which Oryx will be merged
with and into the  Company  on the  terms and  conditions  stated  therein  (the
"Merger"),  and (ii) a Stock Option Agreement,  dated as of October 14, 1998 (as
it may be further amended, supplemented or otherwise modified from time to time,
the "Option  Agreement")  pursuant  to which the  Company  will grant to Oryx an
option  to  purchase  shares  of Common  Stock of the  Company  on the terms and
conditions stated therein;

     WHEREAS,  the Merger  Agreement  requires that the Company amend the Rights
Agreement to the extent  necessary to provide that the  approval,  execution and
delivery of the Merger Agreement and the Option Agreement,  and the consummation
of the transactions  contemplated thereby, will not (i) cause Oryx or any of its
affiliates to become an Acquiring Person or (ii) cause the occurrence of a Stock
Acquisition Date or Distribution Date; and

     WHEREAS,  the  Board of  Directors  has  determined  that it is in the best
interest of the Company and its  stockholders  to amend the Rights  Agreement to
exempt the Merger, the Merger Agreement and the Option Agreement, and all of the
transactions contemplated thereby, from the application of the Rights Agreement.

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*        The Liberty National Bank & Trust Co. of Oklahoma City was merged into
         Bank One Trust Company, N.A., effective December 5, 1997.

                                A G R E E M E N T

     NOW THEREFORE, the Company hereby amends the Rights Agreement as follows:

     1. Section 1(a) of the Rights  Agreement is hereby  modified and amended by
adding the following proviso at the end of the first sentence thereof:

                  ";  provided,  further,  that neither Oryx Energy  Company,  a
                  Delaware  corporation  ("Oryx"),  nor any of its Affiliates or
                  Associates shall be deemed to be an Acquiring Person by virtue
                  of (i) the  approval,  execution or delivery of the  Agreement
                  and Plan of Merger  dated as of October  14,  1998,  as may be
                  amended, supplemented or otherwise modified from time to time,
                  between the Company and Oryx (the  "Merger  Agreement"),  (ii)
                  the  approval,  execution  or  delivery  of the  Stock  Option
                  Agreement  dated as of October  14,  1998,  as may be amended,
                  supplemented or otherwise  modified from time to time, between
                  the Company and Oryx pursuant to which the Company has granted
                  to Oryx an option to  purchase  shares  of Common  Stock  (the
                  "Option  Agreement") or (iii) the  consummation  of any of the
                  transactions  contemplated  by  the  Merger  Agreement  or the
                  Option Agreement."

     2. The Rights  Agreement is hereby further modified and amended by adding a
new Section 35 to the end thereof to read in its entirety as follows:

                  "Section 35. Merger  Agreement and Option Agreement with Oryx.
                  Notwithstanding  any other provision of this Rights Agreement,
                  as  amended  by this  Amendment,  neither  (i)  the  approval,
                  execution  or  delivery  of  the  Merger   Agreement  nor  the
                  consummation of any of the transactions  contemplated thereby,
                  nor (ii) the  approval,  execution  or  delivery of the Option
                  Agreement  nor  the  consummation  of any of the  transactions
                  contemplated  thereby,  is or shall be  deemed  to be an event
                  described in Section 11(a)(ii) or Section 13 hereof,  nor will
                  such performance or consummation result in the occurrence of a
                  Stock  Acquisition  Date,  a  Distribution  Date or any  other
                  separation of the Rights from the underlying Common Stock, nor
                  entitle or permit the  holders of the Rights to  exercise  the
                  Rights or  otherwise  affect the rights of the  holders of the
                  Rights or  otherwise  affect the rights of the  holders of the
                  Rights,  including  giving the holders of the Rights the right
                  to acquire  securities of any party to the Merger Agreement or
                  the Option Agreement."

     3. This Amendment shall become effective as of the date of, and immediately
prior to the execution of, the Merger Agreement and the Option Agreement.

     4. 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.

     5. This  Amendment may be executed in any number of  counterparts,  each of
which shall be an original,  but such counterparts shall together constitute one
and the same instrument.

     6. Terms not defined herein shall,  unless the context otherwise  requires,
have the meanings assigned to such terms in the Rights Agreement.

     7. In all respects not  inconsistent  with the terms and provisions of this
Amendment,  the Rights  Agreement  is hereby  ratified,  adopted,  approved  and
confirmed. In executing and delivering this Amendment, the Rights Agent shall be
entitled to all the privileges and immunities  afforded to the Rights  Agreement
under the terms and conditions of the Rights Agreement.

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     IN WITNESS  WHEREOF,  this  Amendment has been duly executed by the Company
and the Rights Agent as of the day and year first written above.


                                         KERR-McGEE CORPORATION


                                         By: /s/ Luke R. Corbett
                                             -------------------
                                             Name:   Luke R. Corbett
                                             Title:  Chairman and CEO

                                         BANK ONE TRUST COMPANY, N.A.


                                         By: /s/ M. E. Allan
                                             ---------------
                                             Name: M. E. Allan
                                             Title:  Vice President