<PAGE>



                                                                Exhibit 10.15(b)






                       MILLENNIUM CHEMICALS GRANDFATHERED

                     SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN

                 (As amended and restated as of January 1, 1999)











<PAGE>


Millennium Chemicals
Grandfathered Supplemental Executive Retirement Plan
(As amended and restated as of January 1, 1999)

Contents

<TABLE>
<CAPTION>
--------------------------------------------------------------------------------
Section                                                                Page
<S>      <C>                                                          <C>
         Section 1. Definitions

         Introduction

1.1      Average Final Compensation                                      2
1.2      Base Compensation                                               2
1.3      Company                                                         2
1.4      Committee                                                       2
1.5      Credited Service                                                2
1.6      Deferred Retirement Date                                        2
1.7      Early Retirement Date                                           3
1.8      Normal Retirement Date                                          3
1.9      Participant                                                     3
1.10     Pension Offset                                                  3
1.11     Plan                                                            3
1.12     Qualified Plan                                                  3
1.13     Retirement Date

         Section 2. Participation

2.1      Participation                                                   4
2.2      Continuation of Participation                                   4

         Section 3. Retirement Date

3.1      Normal Retirement Date                                          5
3.2      Deferred Retirement Date                                        5
3.3      Early Retirement Date                                           5

         Section 4. Retirement Benefits

4.1      Normal Retirement Benefit                                       6
4.2      Deferred Retirement Benefit                                     6
4.3      Early Retirement Date                                           6
4.4      Adjusted Age and Credited Service                               7
</TABLE>

i






<PAGE>


Millennium Chemicals
Grandfathered Supplemental Executive Retirement Plan
(As amended and restated as of January 1, 1999)

Contents
<TABLE>
<CAPTION>
--------------------------------------------------------------------------------
Section                                                                Page
<S>      <C>                                                          <C>
         Section 5. Death Benefits

5.1      Prior to Retirement                                             8
5.2      After Retirement                                                9

         Section 6. In Event of Termination Of Employment

6.1      Termination Prior to Retirement                                 10
6.2      Termination after Eligibility for Retirement                    10

         Section 7. Time And Form Of Benefit Payment

7.1      Normal Form of Benefit                                          11
7.2      Optional Forms of Benefit                                       11

         Section 8. Provision Of Benefits

8.1      Participant Contributions                                       12
8.2      Fund                                                            12

         Section 9.  Administration Of The Plan

9.1      Powers and Duties of the Committee                              13

         Section 10. Miscellaneous

10.1     Prohibition against Encumbrance                                 14
10.2     Right of Participant                                            14
10.3     Change in Control                                               14

         Section 11. Amendment Or Termination Of the Plan

11.1     Amendment                                                       17
11.2     Termination                                                     17

         Schedule A
</TABLE>


ii






<PAGE>


                                  INTRODUCTION


         This Supplemental Executive Retirement Plan was first adopted by the
Company on October 1, 1992 when it was a Member of the Hanson Industries
controlled group of companies.

         It is intended that the Plan be a non-qualified, unfunded, deferred
compensation plan for "a select group of management or highly compensated
employees" as that term is used in the Employee Retirement Income Security Act
of 1974.

         The purpose of the Plan is to provide a minimum level of retirement
income from the Company, in addition to other sources of capital accumulation.





                                        1






<PAGE>


                                    SECTION 1

                                   DEFINITIONS

         The following words and phrases as used herein have the following
meanings unless a different meaning is plainly required by the context:

1.11 "Average Final Compensation" means the highest average annual Base
     Compensation for any 5 calendar years in the final 10 years of employment
     with the Company or, if greater, the average annual Base Compensation for
     the 60 month period immediately preceding his or her Retirement Date.

1.2  "Base Compensation" means, for any period, the base rate of pay paid to the
     Participant for such period, plus all bonuses paid under the Company's
     annual bonus incentive plan in such period (but not including any
     supplemental executive bonus, any long-term incentive bonus, or "top hat"
     bonus), plus any such base pay or annual bonus that would have been payable
     in such period if such base pay or annual bonus had not been deferred at
     the election of the Participant; provided, however, that Base Compensation
     shall not include the subsequent payment of any deferred base pay or annual
     bonus which has been included in Base Compensation for any previous period,
     and provided, further, that Base Compensation shall not include any
     termination or severance pay, prizes, awards, grievance settlements, living
     allowances, mortgage assistance, executive perquisites, restricted stock,
     stock options, distributions under any performance incentive compensation
     plan or policy other than the Company's annual performance incentive plan
     as described above, and such other extraordinary items of remuneration as
     the Committee shall determine from time to time.

1.3  "Company" means Millennium America Holdings Inc.

1.4  "Committee" means the Millennium Chemicals Benefits Administration
     Committee.

1.5  "Credited Service" means a Participant's period (or periods) of employment
     with the Company subject to a maximum of 25 years. Credited Service shall
     be computed in years and full months.

1.6  "Deferred Retirement Date" means the first day of the month coincident with
     or immediately following the date a Participant actually retires after his
     or her Normal Retirement Date pursuant to the provisions of Section 3.2
     (Deferred Retirement Date).


                                        2






<PAGE>


1.7  "Early Retirement Date" means the first day of the month coincident with or
     immediately following the date a Participant retires prior to his or her
     Normal Retirement Date pursuant to the provisions of Section 3.3 (Early
     Retirement Date).

1.8  "Normal Retirement Date" means the first day of the month next following
     the date on which a Participant attains his or her 65th birthday.

1.9  "Participant" means a person who is included in the Plan as provided in
     Section 2 (Participation).

1.10 "Pension Offset" means the annual amount of pension that a Participant is
     entitled to receive, in the form of straight life annuity determined at
     Normal Retirement Date, from the Qualified Plan.

l.11 "Plan" means the Millennium Chemicals Grandfathered Supplemental Executive
     Retirement Plan.

1.12 "Qualified Plan" means the Millennium Chemicals Inc. Pension Plan (the
     terms of which appear in the Millennium Chemicals Inc. Consolidated
     Retirement Plan as modified by Appendix XX thereto) or any successor plan.

1.13 "Retirement Date" means the Early Retirement Date, the Normal Retirement
     Date or the Deferred Retirement Date, whichever is applicable.


                                        3






<PAGE>


                                    SECTION 2

                                  PARTICIPATION


2.1  Participation:

     Participants will be limited to individuals who are listed in Schedule A
hereto, as such schedule may be amended from time to time by the Committee.

2.2  Continuation of Participation:

     (a)  A person who has become a Participant in accordance with Section 2.1
          shall, except as provided in (b) below, continue as a Participant as
          long as he continues in the employment of the Company and thereafter
          as long as he is entitled to benefits under the Plan.

     (b)  The Committee may, in its sole discretion remove a Participant from
          active participation in the Plan if the Participant is no longer an
          Executive Officer. In this event, any benefits accrued under this Plan
          will be vested and payable at the Participant's Retirement Date in
          accordance with Section 6. Notwithstanding anything herein to the
          contrary, if a Participant's employment is terminated for cause or
          mismanagement as determined by the Committee, or if the Participant is
          convicted of a felony or if the Participant's employment terminates
          prior to retirement as provided in Section 6.1, all rights under this
          Plan shall be forfeited.

     (c)  After a Participant commences retirement benefits in accordance with
          Section 4, the Committee, in its sole discretion, may cease payment of
          benefits under this Plan if the Committee determines that the
          Participant is acting in bad faith against the Company or has filed
          any legal suits, complaints or grievances against the Company in any
          court of law, tribunal or with any federal, state or municipal agency.

     (d)  Benefits will cease to accrue for all Participants under the Plan on
          January 1, 1999 except for those persons who were age 55 or older and
          Executive Officers of Millennium Chemicals Inc. on December 31, 1998.


                                        4






<PAGE>


                                    SECTION 3

                                 RETIREMENT DATE


3.1  Normal Retirement Date:

     A Participant who retires on his or her Normal Retirement Date shall be
     entitled to a benefit as determined in accordance with Section 4.1 (Normal
     Retirement Benefits).

3.2  Deferred Retirement Date:

     A Participant whose employment with the Company continues beyond his or her
     Normal Retirement Date and whose entitlement to benefits under the Plan has
     not been forfeited in accordance with (b) of Section 2.2 (Continuation of
     Participation), may retire on a Deferred Retirement Date and shall be
     entitled to a benefit in accordance with Section 4.2. (Deferred Retirement
     Benefit).

3.3  Early Retirement Date:

     A Participant who has attained age 60 and accrued 5 or more years of
     Credited Service, may retire at an Early Retirement Date. In such case, the
     Participant shall be entitled to a benefit as determined with Section 4.3
     (Early Retirement Benefit).


                                        5






<PAGE>


                                    SECTION 4

                               RETIREMENT BENEFITS


4.1  Normal Retirement Benefit:

     The annual amount of benefit for a Participant retiring on his or her
     Normal Retirement Date shall be equal to (a) less (b), times (c), less (d)
     as follows:

     (a)  66 2/3% of his or her Average Final Compensation,

     (b)  less 50% of his or her Primary Social Security Benefit,

     (c)  years of Credited Service (maximum 25), divided by 25,

     (d)  the Pension Offset; provided, however, that the annual amount of
          benefit payable hereunder shall not exceed 45% of Average Final
          Compensation as defined herein; and, provided, further, that each
          Participant shall only be entitled to receive a benefit under this
          Plan if such benefit is greater than the benefit that such Participant
          is entitled to receive under the Millennium Chemicals Supplemental
          Executive Retirement Plan (the "PEP SERP"), in which case such
          Participant shall receive only the benefits to which he or she is
          entitled to receive under this Plan, and such Participants shall not
          be entitled to receive any benefits under the PEP SERP.

4.2  Deferred Retirement Benefit:

     If a Participant remains in employment after his or her Normal Retirement
     Date and is entitled to a benefit in accordance with Section 3.2 (Deferred
     Retirement Date), benefit payments shall be postponed until the
     Participant's actual retirement on the Deferred Retirement Date. At such
     Deferred Retirement Date, the Participant shall be entitled to the benefit
     computed under Section 4.1 based on Credited Service to the Deferred
     Retirement Date.

4.3  Early Retirement Date

     A Participant retiring prior to his or her Normal Retirement Date, as
     provided in Section 3.3 (Early Retirement Date), shall be entitled to
     receive a benefit, commencing on such Normal Retirement Date, equal to the
     amount computed under Section 4.1 based on his or her Average Final
     Compensation and Credited Service determined on such Early Retirement Date.


                                        6






<PAGE>


     In lieu of such benefit commencing on the Normal Retirement Date, the
     Participant may elect to have such benefit commence on his or her Early
     Retirement Date. In such case, the Participant's benefit shall be reduced
     by 1/2% per month by which such Early Retirement Date precedes his or her
     Normal Retirement Date.

4.4  Adjusted Age and Credited Service:

     The Committee may, in its sole discretion, determine an adjusted Credited
     Service and/or an adjusted age for the Participant. The adjusted Credited
     Service may be 1, 2, 3, 4 or 5 years more than the actual Credited Service
     (subject to the 25 years maximum for Credited Service). The adjusted age
     may be 1, 2, 3, 4 or 5 years more than his or her actual age.

     In determining the amount of pension in accordance with Section 4, a
     Participant's adjusted age and adjusted Credited Service shall be used as
     if they were his or her actual age and Credited Service.


                                        7






<PAGE>


                                   SECTION 5.

                                 DEATH BENEFITS

5.1  Prior to Retirement:

     Upon the death of a Participant while an active employee, his or her
     surviving spouse, if any, shall be entitled to a benefit commencing on the
     first day of the month following the Participant's date of death and
     continuing thereafter for the lifetime of the surviving spouse. The amount
     of the benefit payable to the surviving spouse shall be equal to the
     benefit determined under Section 4.1 (Normal Retirement Benefit) based on
     such Participant's Average Final Compensation and Credited Service, each
     determined as of the date of death, multiplied by an Early Commencement
     Percentage based on the Participant's age at date of death in accordance
     with the table below and further reduced to reflect the actuarial
     equivalent charge for the election of a 100% joint and survivor option
     pursuant to the option factors under the Qualified Plan.

<TABLE>
<CAPTION>
     Deceased Employee's                           Early
                                                Commencement
         Age at Death                            Percentage
     --------------------                        ----------
             <S>                                  <C>
              60                                     64
              61                                     70
              62                                     76
              63                                     82
              64                                     94
              65                                    l00%
</TABLE>

     If at any time on or after the Participant's death there is no surviving
     spouse but there are one or more dependent children under age 19 or, if a
     full-time college student, age 23, the benefit which would have been paid
     to a surviving spouse shall be paid in equal shares to the dependent
     children as long as each shall qualify, until such ages 19 or 23.

     Benefit payments to a dependent child shall cease upon the earlier of (a)
     the last day of the month in which such child reaches such age 19 or 23, or
     (b) the last day of the month preceding the month in which such child dies.
     The share payable in respect of any such child shall subsequently increase
     by reason of the subsequent cessation of payments in respect of any other
     such child.


                                        8






<PAGE>


     For the purposes of determining dependency, a child shall be deemed
     dependent if the Participant provided one-half or more of such child's
     support during the year immediately prior to such Participant's death. The
     Committee shall determine on a uniform and non-discriminatory basis the
     dependence of any person to whom a benefit may be payable under Section 5.l
     and such determination shall be final and conclusive.

5.2  After Retirement:

     There is no benefit payable under the Plan in the event of the
     Participant's death after his or her retirement benefit has commenced
     unless an option is in effect in accordance with Section 7.2 (Optional
     Forms of Benefits).



                                        9






<PAGE>


                                    SECTION 6

                      IN EVENT OF TERMINATION OF EMPLOYMENT


6.1  Termination Prior to Retirement:

     If a Participant's emp1oyment with the Company ceases for any reason and he
     is not eligible for benefit under the provisions of Section 3 (Retirement
     Date), or Section 6 (Death Benefits), no benefits shall become payable to
     such Participant under this Plan.

6.2  Termination after Eligibility for Retirement:

     A Participant whose employment with the Company ceases for any reason other
     than death and who is eligible to retire under the provisions of Section 3
     (Retirement Date), shall be deemed to have retired or to have been retired
     by the Company and he shall be entitled to the appropriate benefits,
     subject to any possible forfeiture of benefits pursuant to Section 2.2.



                                       10






<PAGE>


                                    SECTION 7

                        TIME AND FORM OF BENEFIT PAYMENT


7.1  Normal Form of Benefit:

     Except as otherwise provided in Section 7.2, the retirement benefit shall
     be payable as a monthly annuity as of the last day of each calendar month
     for the life of the Participant with benefits ceasing upon the
     Participant's death.

7.2  Optional Forms of Benefit:

     If a Participant is entitled to a benefit from the Qualified Plan, the
     benefit under this Plan may be paid in the same form as the Qualified
     Plan's benefit is payable so long as Committee approval is secured. If such
     form of payment is other than a straight life annuity, the amount of
     pension otherwise payable under this Plan sha1l be adjusted in the same
     manner that benefits are to be adjusted under the Qualified Plan.



                                       11






<PAGE>


                                    SECTION 8

                              PROVISION OF BENEFITS


8.1  Participant Contributions:

     Participants shall make no contributions under the Plan.

8.2. Fund:

     Benefit payments from the Plan will be made from the general assets of the
     Company in accordance with such arrangements as the Company may deem
     necessary and proper to fulfill its agreement hereunder.



                                       12






<PAGE>


                                    SECTION 9

                           ADMINISTRAT10N OF THE PLAN


9.1  Powers and Duties of the Committee

     The Committee, in addition to all the powers and duties specified in the
     various provisions of the Plan, shall have the exclusive right to interpret
     the Plan and to decide any matter arising in connection with the
     administration of the Plan.




                                       13






<PAGE>


                                   SECTION 10

                                  MISCELLANEOUS

10.1 Prohibition against Encumbrance:

     Except in the case of a court order which meets the requirements of a
     "qualified domestic relations order" as defined in Section 414(p) of the
     Internal Revenue Code of 1986, no benefit under the Plan shall be
     a1ienated, assigned, disposed of, or in any manner encumbered while in the
     possession and control of the Company. If the interest of any Participant
     or Participant's beneficiary would, but for this Section 10.1, cease in
     whole or in part to be enjoyed by such individual, the Committee, in its
     sole discretion, may direct that the funds constituting such interest be
     withheld or it may expend from such funds for the direct maintenance and
     support of the Participant, such Participant's spouse, children or their
     dependents as, in the Committee's sole discretion, it deems fit and proper.

10.2 Right of Participant:

     Neither the adoption of the Plan nor its operation shall in any way affect
     the right and power of the Company to dismiss or otherwise terminate the
     employment, or change the terms of employment, or amount of compensation,
     of any Participant at any time for any reason.

10.3 Change in Control

     The Plan will terminate effective on the close of business 30 days
     following a Change in Control, as hereinafter defined. Upon such Change in
     Control, section 11.1 shall become inoperative and, in addition, any
     modification or amendment adopted within six months prior to the Change in
     Control shall be void with respect to any specific Participant affected
     thereby unless approved by such Participant. Upon such termination, each
     Participant (including each Participant whose employment was terminated
     within six months prior to such Change in Control by the Employer without
     Cause, or due to disability, or voluntarily for good reason as determined
     by the Committee, and each Participant that has experienced a Change of
     Control pursuant to a separate written "Change in Control" agreement with
     the Company or any subsidiary of the Company) will be deemed retired
     pursuant to section 5.1, based on Benefit Service through the termination
     date. A lump sum payment that is the actuarial equivalent of each
     Participant's benefit payable under this Plan calculated using the prime
     rate of interest at Citigroup, Inc. as of the date of the Change in Control
     or 6%,


                                       14






<PAGE>


     whichever is less, as the discount rate to determine the present value of
     accrued benefits, shall be paid as soon as practicable following the date
     of the Change in Control, but in no event later than 90 days thereafter.
     All other actuarial assumptions and calculation methods to be used shall be
     those in effect as at the last actuarial valuation of the Qualified Plan
     and based on the Qualified Plan document prior to such Change in Control.

     For purposes of this Section 10.3 "Change in Control" is defined as
     follows:

          The term "Change in Control" shall mean (i) any "person" as such term
     is used in Sections 13(d) and 14(d) of the Securities Exchange Act of 1934
     ("Exchange Act") (other than Millennium Chemicals Inc. (the "Parent"), any
     trustee or other fiduciary holding securities under any employee benefit
     plan of the Parent or any company owned, directly or indirectly, by the
     stockholders of the Parent in substantially the same proportions as their
     ownership of Common Stock of the Parent), becoming the "beneficial owner"
     (as defined in Rule 13d-3 under the Act), directly or indirectly, of
     securities of the Parent representing twenty-five percent (25%) or more of
     the combined voting power of the Parent's then outstanding securities; (ii)
     during any period of two consecutive years, individuals who at the
     beginning of such period constitute the Board of Directors of the Parent,
     and any new director (other than a director designated by a person who has
     entered into an agreement with the parent to effect a transaction described
     in clause (i), (iii), or (iv) of this paragraph or a director whose initial
     assumption of office occurs as a result of either an actual or threatened
     election contest (as such terms are used in Rule 14a-11 of Regulation 14A
     promulgated under the Exchange Act) or other actual or threatened
     solicitation of proxies or consents by or on behalf of a person other than
     the Board of Directors of the Parent) whose election by the Board of
     Directors of the Parent or nomination for election by the Parent's
     stockholders was approved by a vote of at least two-thirds of the Directors
     then still in office who either were directors at the beginning of the
     two-year period or whose election or nomination for election was previously
     so approved, cease for any reason to constitute at least a majority of the
     Board of Directors of the Parent; (iii) the merger or consolidation of the
     Parent with any other corporation, other than a merger or consolidation
     which would result in the voting securities of the Parent outstanding
     immediately prior thereto continuing to represent (either by remaining
     outstanding or by being converted into voting securities of the surviving
     entity) more than fifty percent (50%) of the combined voting power of the
     voting securities of the Parent or such surviving entity outstanding
     immediately after such merger or consolidation provided, however, that a
     merger or consolidation effected to implement a recapitalization of the
     Parent (or similar transaction) in which no person (other than those
     covered by the exceptions in (i) above) acquires more than twenty-five
     percent (25%) of the


                                       15






<PAGE>


     combined voting power of the Parent's then outstanding securities shall not
     constitute a Change in Control or (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. "Subsidiary" has the meaning set forth
     in Section 424(f) 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. Notwithstanding any of the foregoing, the sale or
     disposition of all or any part of the Parent's interests in Equistar
     (separately or together with the sale or disposition of the business of the
     Company or any of the assets of the Company) shall not constitute a Change
     in Control. Only one (1) Change in Control may take place under this Plan.


                                       16






<PAGE>


                                   SECTION 11

                      AMENDMENT OR TERMINATION OF THE PLAN


11.1 Amendment:

     The Board of Directors reserves the right at any time and from time to
     time, to modify or amend, in whole or in part, any or all of the provisions
     of the Plan but no such amendment shall adversely affect any Participant's
     or Participant's beneficiary's rights to benefits accrued under the Plan
     prior to the effective date of the amendment.

11.2 Termination:

     The Board of Directors shall have the right to terminate the Plan at any
     time provided that such action shall not adversely affect any Participant's
     or Participant's beneficiary's rights to benefits accrued under the Plan
     prior to such action.


                                       17






<PAGE>



                                   SCHEDULE A


William M. Landuyt

Robert E. Lee

George H. Hempstead, III

Richard A. Lamond

John E. Lushefski

C. William Carmean

Marie S. Dreher

A. Michelson Foster

Christine F. Wubbolding

Francis V.  Lloyd

James Lofredo



                                       18