Exhibit 10.1

AMENDMENT NUMBER ONE

TO THE

ANNUAL INCENTIVE PLAN OF CHEVRON PHILLIPS CHEMICAL COMPANY LLC

WHEREAS, effective January 1, 2001, Chevron Phillips Chemical Company LLC (the “Company”) established the Annual Incentive Plan of Chevron Phillips Chemical Company LLC (the “Plan”); and

WHEREAS, pursuant to Section 2 of the Plan, the Compensation Committee of the Board of Directors of the Company reserves the right to amend the Plan from time to time.

NOW THEREFORE BE IT RESOLVED:

1.             Effective January 1, 2005, Section 1, entitled “Target Awards”, of Schedule A of the Plan is deleted in its entirety, and replaced with the following new Section 1:

1.  Target Awards

The following target award schedule shall apply to Participants in the Plan for the Plan Year 2005 and for subsequent Plan Years unless changed by the Board of Directors or Compensation Committee:

[SIGNATURE ON NEXT PAGE]

1

IN WITNESS WHEREOF, the Company has caused this First Amendment to be executed this        day of April, 2005.

2

ANNUAL INCENTIVE PLAN

OF

CHEVRON PHILLIPS CHEMICAL COMPANY LLC

Revised by BOD October 24, 2002

ANNUAL INCENTIVE PLAN

OF

CHEVRON PHILLIPS CHEMICAL COMPANY LLC

Table of Contents

ii

ANNUAL INCENTIVE PLAN

OF

CHEVRON PHILLIPS CHEMICAL COMPANY LLC

PURPOSE

The purpose of the Annual Incentive Plan (the “Plan”) is to attract, motivate, and retain qualified management personnel by providing to them an annual incentive compensation plan that will provide competitive compensation opportunities similar to those of comparable companies in the chemical industry, align the interests of key management personnel with the interests of the Company’s shareholders, and assist the Company in achieving its goal of being the top performer in each of its businesses.

The Plan is intended to be a compensation plan for a select group of management or other highly-compensated employees, within the meaning of ERISA.

The Plan shall be effective as of January 1, 2001.

1.             Interpretation and Definitions

1.1          General.

(a)           Interpretation.  Unless a clear contrary intention appears, for purposes of construction of this Plan and all related Plan Documents:

(i)            the singular number includes the plural number and vice versa;

(ii)           reference to any person includes such person’s successors and assigns but, if applicable, only if such successors and assigns are permitted by the Plan Documents, and reference to a person in a particular capacity excludes such person in any other capacity or individually;

(iii)          reference to any gender includes each other gender;

(iv)          reference to any agreement, document or instrument means such agreement, document or instrument as amended or modified and in effect from time to time in accordance with the terms thereof;

(v)           reference to any law means such law as amended, modified, codified, replaced or reenacted, in whole or in part, and in effect from time to time, including rules and regulations promulgated thereunder, and reference to any section or other provision of any law means that provision of such law from time to time in effect and constituting the substantive amendment, modification, codification, replacement or reenactment of such section or other provision;

(vi)          reference in any Plan Document to any article, section, appendix, schedule or exhibit means such article or section thereof or appendix, schedule or exhibit thereto;

(vii)         “hereunder”, “hereof”, and words of similar import shall be deemed references to a Plan Document as a whole and not to any particular article, section or other provision thereof;

(viii)        “including” (and with the correlative meaning “include”) means including without limiting the generality of any description preceding such term;

(ix)           “or” is not exclusive;

(x)            relative to the determination of any period of time, “from” means “from and including” and “to” means “to but excluding;” and

(xi)           references to days, weeks, months, quarters and years are references to such periods as determined by the Gregorian calendar.

(b)           Accounting Terms.  In each Plan Document, unless expressly otherwise provided, accounting terms shall be construed and interpreted, and accounting determinations and computations shall be made, in accordance with generally accepted accounting principles.

(c)           Conflict in Plan Documents.  If there is any conflict between any two or more Plan Documents, such Plan Documents shall be interpreted and construed, if possible, so as to avoid or minimize such conflict but, to the extent (and only to the extent) of such conflict, the Plan Document dealing most specifically with the matter as to which there is a conflict shall prevail and control.

1.2          Definitions

(a)           “Affiliate” means an entity which controls, is controlled by, or is under common control with, the Company. For purposes hereof, an entity shall be deemed to control another entity if the first entity directly or indirectly owns at least fifty percent (50%) of the stock, partnership interests or membership interests of the second entity, or if, by the ownership of stock, by contract or otherwise, the first entity has the right to select the management or direct the policies of the second entity.

(b)           “Award” means an award of cash made pursuant to the Plan.

(c)           “Board” means the Board of Directors of the Company.

(d)           “Bonus Level Employee” means, (i) with respect to Employees on the U.S. Dollar payroll of a Participating Employer, those Employees who are employed within

2

pay grades 90 through 99, and (ii) with respect to Employees who are not on a U.S. Dollar payroll, those Employees who are employed within pay grades which are deemed by the Compensation Committee to be equivalent to grades 90 through 99.

(e)           “ChevronTexaco” means ChevronTexaco Corporation or such entity as may be controlled by ChevronTexaco that directly or indirectly holds a membership interest in the Company.

(f)            “Change in Control” of the Company shall mean an occurrence which the Board determines, in its sole discretion, to be a change of control and generally may include instances when: (i) any person or persons acting together as a single entity, other than ChevronTexaco Corporation or ConocoPhillips, acquires more than fifty percent (50%) of the Company’s assets or voting ownership interests; (ii) during any period of two consecutive years, individuals who at the beginning of the two-year period constitute the Board cease for any reason to constitute a majority of the Board; (iii) a merger or consolidation of the Company with any other corporation or entity is consummated; or (iv) the owners of the Company approve a plan of complete liquidation or dissolution of the Company or an agreement for the sale or disposition by the Company of all or substantially all of the Company’s assets.

(g)           “Committee” or “Compensation Committee” means the Compensation Committee of the Board.

(h)           “Company” means the Chevron Phillips Chemical Company LLC and any successor entity.

(i)            “Date of Termination” means the date on which a Participant ceases to be a regular, full-time Employee.

(j)            “Disability” means disability as determined under the Long-Term Disability Plan of Chevron Phillips Chemical Company LP.

(k)           “Employee” means any full-time employee of a Participating Employer.

(l)            “ERISA” means the Employee Retirement Income Security Act of 1974.

(m)          “Layoff” means termination of employment by reason of layoff pursuant to the Chevron Phillips Chemical Company LP Layoff Pay Plan or a similar layoff pay plan adopted by a Participating Employer.

(n)           “Participant” means an Employee to who has been designated as a participant pursuant to Section 3.

3

(o)           “Participating Employer” means any direct or indirect subsidiary entity of the Company which, with the Company’s consent, has adopted the Plan.

(p)           “ConocoPhillips” means ConocoPhillips, or such entity as may be controlled by ConocoPhillips that directly or indirectly holds a membership interest in the Company.

(q)           “Plan” means the Chevron Phillips Chemical Company LLC Annual Incentive Plan.

(r)            “Plan Year” means a period of twelve (12) months beginning on January 1 of any year.

(s)           “Plan Document” means this Plan, any Administrative Procedures that may from time to time be adopted by the Committee, and any other document defining the rights and liabilities of any Participant.

(t)            “Retirement” means retirement pursuant to the Retirement Income Plan of Chevron Phillips Chemical Company LP, or any retirement plan of any Participating Employer.

(u)           “Salary” means the annualized base rate of a Participant as of December 31 of the Plan Year with respect to which an Award is made or, in the case of the termination of a Participant’s employment by reason of Disability, Retirement, Layoff or death, the base rate of the Participant on the date of such Participant’s Termination of Service.

(v)           “Termination of Service” means the cessation of a Participant’s status as an Employee for any reason.

2.             Administration

(a)           The Plan shall be administered by the Committee.

(b)           The Committee may establish, from time to time and at any time, subject to the limitations of the Plan as set forth herein, such rules and regulations, and amendments and supplements thereto, as it deems necessary to comply with applicable law and for the proper administration of the Plan.

(c)           A majority of the members of the Committee shall constitute a quorum.  The vote of a majority of a quorum shall constitute action by the Committee provided that at least one member of the Committee appointed by ChevronTexaco and one member appointed by ConocoPhillips concurs therein.

(d)           No member of the Board or the Committee shall be personally liable for any action taken, or determination made, in respect of the Plan in good faith. Each

4

member of the Board and the Committee shall be fully justified in relying upon or acting in good faith upon any opinion, report or information furnished in connection with the Plan by any accountant, counsel, or other specialist (including financial officers of the Company, whether or not such persons are Participants in the Plan).

(e)           This Plan may be adopted by such subsidiary entities of the Company as the Board or Committee may approve, whereupon such entities shall become Participating Employers. The Committee shall administer the Plan for the benefit of all Participating Employers.

(f)            The Committee may delegate to the officers or other employees of the Company or any Participating Employer such authorities and responsibilities with respect to the administration of the Plan as it may deem appropriate.

(g)           Determinations by the Committee and its designees with respect to the construction operation or interpretation of any Plan Document shall be final, binding and conclusive on the Company, Participating Employers, Employees and Participants.

3.             Eligibility and Participation

(a)           Except as hereinafter provided, all Bonus Level Employees shall be Participants in the Plan.

(b)           Notwithstanding Section 3(a), the Committee may from time to time select additional Employees or classes of Employees for participation in the Plan, and may direct that specific Bonus Level Employees, or classes of Bonus Level Employees be removed from participation. Any such determination may be made at any time prior to the payment of awards with respect to any Plan Year, and may be made with respect to participation during all or any part of any Plan Year.

4.             Awards and Payment of Awards

(a)           As soon as practicable following the beginning of each Plan Year, the Committee shall (i) make such determinations as it may deem appropriate with respect to the selection of Participants for such Plan Year; (ii) establish target awards for such Participants; and (iii) establish performance measures under which determinations may be made as to whether awards will be paid for such Plan Year and, if so, the amounts to be paid.

(b)           The matters described in Section 4(a) applicable to any Plan Year shall be set forth in an Administrative Procedures document.  The Administrative Procedures for the 2001 Plan Year are attached hereto.  Administrative Procedures applicable to subsequent Plan Years, when adopted by the Committee, shall be substituted for the Administrative Procedures attached hereto.

5

(c)           Awards, if determined to be payable pursuant to the Administrative Procedures, shall be payable to Participants as soon as practicable following the date on which such determination is made for any Plan Year. All such Awards shall be payable in cash, unless another form of payment is specified by the Committee. Notwithstanding the foregoing, Participants may elect to defer receipt of all or part of any Award, and to have the same credited to an account under the Company’s nonqualified deferred compensation plan, provided that such Participant is otherwise eligible to participate in such plan. Any such election must be made at such time, and in such manner, as may be specified by the Committee.

(d)           In the event of a Participant’s termination of employment by reason of Retirement, Disability, Layoff or death, or by reason of such Participant’s transfer to the payroll of an Affiliate which is not a Participating Employer, the award, if any, payable to such Participant for the Plan Year in which such termination occurs shall be equal to the product of (i) the Award that would have been payable to such Participant if such termination had not occurred, and (ii) a fraction, the numerator of which is the number of days in such Plan Year for which the Participant participated in the Plan, and the denominator of which is 365. Notwithstanding the foregoing, the Committee may, in its sole discretion, determine that a greater or lesser amount shall be paid. Any amount payable by reason of a Participant’s death, shall be paid to such Participant’s estate or to such other individuals or entities as the Committee shall direct.

(e)           In the event of a Participant’s termination of employment, prior to the payment of Awards for any Plan Year, for reasons other than Retirement, Disability, Layoff or death, the Award, if any, which would have been payable for such Plan Year shall be forfeited; provided, the Committee may in its sole discretion determine to pay all or any portion of any such Award.

(f)            The payment of any Award may be made subject to such conditions as the Committee may specify. Any such conditions may be specified in respect of Participants as a whole, individual Participants, or classes of Participants.

5.             Recapitalization, Merger, and Consolidation; Change in Control

(a)           The existence of this Plan and the Awards granted hereunder shall not affect in any way the right or power of the Company or those entities holding membership interests in the Company to make or authorize adjustments, reorganizations, or other changes in the Company’s capital structure and its business, or any merger or consolidation of the Company, or the dissolution or liquidation of the Company, or any sale or transfer of all or part of its assets or business, or any other corporate act or proceeding, whether of a similar character or otherwise.

6

(b)           In the event of a Change in Control, all target awards outstanding shall thereupon automatically be accelerated and payable in full. The amount of such awards shall be determined in the Committee’s discretion on the assumption that the Plan Year then in effect ended on the date on which the Change in Control occurred. The determination of the Committee that any of the foregoing conditions has been met shall be binding and conclusive on all parties. Notwithstanding the foregoing, in the event that, incident to a Change in Control, provision is made for the transfer of rights under this Plan to another or successor Plan, Participants shall be allowed to make such transfer.

6.             Miscellaneous

(a)           Awards shall be nontransferable and nonassignable, except that such Awards may be transferred (i) by testamentary instrument or by the laws of descent and distribution, or (ii) to such individual or entity as the Committee may designate in the event of a Participant’s death.

(b)           The Board may at any time and from time to time amend the Plan. Any such amendments may be made effective with respect to any Plan Year and with respect to any awards which, as of the date of amendment, have not become payable.

(c)           The establishment of the Plan shall not confer any legal rights upon any Employee or other person to continued employment, nor shall it interfere with the right of the Company or any Participating Employer (which right is hereby reserved) to discharge any Employee and to treat him or her without regard to the effect which that treatment might have upon him or her as a Participant or potential Participant.

(d)           In the event that any Participant engages in any activity which the Committee judges to be detrimental to the Company or any Participating Employer, or otherwise fails to substantially perform his or her obligations as an Employee, the Committee may, at any time prior to payment of an award to a Participant, cancel or reduce the award in whole or in part.

(e)           Neither the adoption of this Plan nor any action of the Board or the Committee shall be deemed to give any person any right to be granted an Award, except as otherwise specifically provided herein.

(f)            The Company shall have the right to deduct from all amounts paid hereunder, any federal, state, local, or other taxes required by law to be withheld with respect to such payments.

(g)           THE VALIDITY, CONSTRUCTION AND EFFECT OF THE PLAN, ANY PLAN DOCUMENTS, AND ANY ACTIONS TAKEN OR RELATING TO THE PLAN SHALL BE DETERMINED IN ACCORDANCE WITH THE

7

LAWS OF THE STATE OF TEXAS APPLICABLE TO CONTRACTS MADE AND TO BE PERFORMED WITHIN SUCH STATE.

(h)           The Company will require any successor (whether direct or indirect, by purchase, merger, consolidation or otherwise) to all or substantially all of the business and/or assets of the Company, expressly to assume and agree to perform the Company’s obligations under this Plan in the same manner and to the same extent that the Company would be required to perform them if no such succession had taken place.

(i)            The Plan shall be unfunded. Neither the Company, any Participating Employer, the Committee, nor the Board shall be required to segregate any assets or secure any liability that may at any time exist under the Plan.

8

SCHEDULE A

Administrative Procedures

Plan Year 2001

1.     Target Awards

The following target award schedule shall apply to Participants in the Plan for the Plan Year 2001 and for subsequent Plan Years unless changed by the Board of Directors or Compensation Committee:

2.     Assignment to Award Units

The Company has established Award Units for purposes of the Employee Incentive Plan (“EIP”) applicable to Employees generally. Each Participant shall be deemed to be a member of the Award Unit through which such individual would participate in the EIP if such individual were not a Participant in this Plan.

3.     Calculation of Awards

The award payable to each Participant shall be determined under the following formula:

Where:

S              is the Participant’s Salary;

T             is the Participants target award, determined under Paragraph 1 above; and

9

X             is the percentage of EIP Target paid to Employees in the Award Unit to which the Participant is assigned.

The above calculation may result in an award ranging from 0% up to 200% of the Target.

4.             Performance and Other Adjustments

In the case of the Chief Executive Officer (“CEO”) or other employees who, in the Committee’s judgment, do not provide services to a single SBU, Facility, Technology Group or Staff, the Committee shall make a special determination as to the manner in which any such individual’s award shall be calculated.

In the event the Committee determines that an individual Participant or group of Participants has made contributions to the success of the Company which deserve special recognition, the Committee may provide for such enhancement of the awards payable to them as the Committee may deem appropriate. Conversely, if the Committee determines that an individual Participant or group of Participants has failed to make such contribution as would have been justified by application of the formula described in paragraph 3 above, the Committee may reduce or cancel the award payable to any such Participant.

10