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                                                                Exhibit 10.12(b)

                            MILLENNIUM CHEMICALS INC.

                                  Amendment To

                       MILLENNIUM SPECIALTY CHEMICALS INC.
              GRANDFATHERED SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN

                                  (the "Plan")


         The Plan shall be, and it hereby is, amended effective June 1, 2002 as
follows:

1.       Section 11.3 Change of Control

         Amend clause (iv) of Section 11.3 to read in its entirety as follows:

         "(iv) the stockholders of the Parent approve a plan of complete
         liquidation of the Parent or the closing of the sale or disposition by
         the Parent of all or substantially all of the Parent's assets other
         than the sale or disposition of all or substantially all of the assets
         of the Parent to one or more Subsidiaries (as defined below) of the
         Parent or to a person or persons who beneficially own, directly or
         indirectly, at least fifty percent (50%) or more of the combined voting
         power of the outstanding voting securities of the Parent at the time of
         the sale or disposition; provided, however, (y) the sale or disposition
         of all or any part of the Parent's interests in Equistar Chemicals, LLP
         ("Equistar") (and all subsequent sales and dispositions of any
         securities or assets received as proceeds thereof, or as proceeds of
         proceeds) shall not be deemed to constitute a Change in Control, and
         (z) if the Parent sells or disposes of all or any part of the
         Parent's interests in Equistar indirectly (either through the sale or
         other disposition of any entity that owns, directly or indirectly, all
         or any part of the Parent's interests in Equistar, or otherwise), then
         the sale or disposition of the Parent's interests in Equistar (and all
         subsequent sales and dispositions of any securities or assets received
         as proceeds thereof, or as proceeds of proceeds) shall be ignored and
         disregarded in determining whether any such Change in Control has
         occurred. By way of illustration, if an indirect subsidiary of the
         Parent that owns the Parent's interests in Equistar together with
         certain other assets is sold, then, in determining whether a Change in
         Control has occurred, all relevant determinations shall be made
         pursuant to the assumption that (y) such subsidiary owns only such
         other assets, and (z) neither such subsidiary nor the Parent owns,
         either directly or indirectly, the interests in Equistar. "Subsidiary"
         shall have the meaning set forth in Section 424 of the Internal Revenue
         Code of 1986, as amended or superseded and the term shall also include
         any partnership, limited liability company or other business entity if
         the Parent owns directly or indirectly, securities or other ownership
         interests representing at least fifty percent (50%) of the ordinary
         voting power or equity or capital interests of such entity."