CABOT OIL & GAS CORPORATION 2004 INCENTIVE PLAN NON-EMPLOYEE DIRECTOR RESTRICTED STOCK UNIT AWARD AGREEMENT

Exhibit 10.1

CABOT OIL & GAS CORPORATION

2004 INCENTIVE PLAN

NON-EMPLOYEE DIRECTOR RESTRICTED STOCK UNIT AWARD AGREEMENT

THIS AGREEMENT (“Agreement”), made as of May 24, 2005 (the “Grant Date”), evidences an award by CABOT OIL & GAS CORPORATION, a Delaware corporation (the “Company”), to                              (the “Grantee”), a nonemployee director of the Company, pursuant to the Cabot Oil & Gas Corporation 2004 Incentive Plan (the ”Plan”). Capitalized terms used and not otherwise defined herein shall have the meaning ascribed thereto in the Plan.

1. Grant of Restricted Stock Units. Effective as of the Grant Date, pursuant to Paragraph 8(a)(ii) of the Plan, the Company has awarded to the Grantee Restricted Stock Units representing a total of 1,950 shares of Common Stock, subject to the conditions and restrictions set forth below and in the Plan (the “Restricted Stock Units”).

2. Restrictions. The Restricted Stock Units granted hereunder to the Grantee may not be sold, assigned, transferred, pledged or otherwise encumbered from the Grant Date unless and until the date that the Grantee obtains the rights of a Stockholder as described in Section 9 of this Agreement. The Grantee shall have a vested right to all of the Restricted Stock Units as of the Grant Date; provided, however, that Common Stock to which such Restricted Stock Units relate shall not be deliverable to the Grantee until the date that the Grantee ceases to be a director of the Board of Directors of the Company.

3. Dividend Credits. During the period of time between the Grant Date and the date on which Grantee receives a distribution of the shares of Common Stock related to the Restricted Stock Units awarded hereunder, the Award of Restricted Stock Units hereunder shall be evidenced by book entry registration. As of each date that dividends are paid with respect to Common Stock, the Grantee shall have an amount credited to his account equal to the amount of the dividend paid per share of Common Stock as of such dividend payment date multiplied by the number of Restricted Stock Units credited to the Grantee’s account immediately prior to such dividend payment date, with such amount to be payable to the Grantee on the earlier of (i) the date of which the Grantee receives his or her next quarterly payment of the annual retainer paid to Grantee for service as a director of the Board of Directors of the Company, or (ii) the date that the Grantee no longer serves as a director of the Company.

4. Beneficiary Designations. The Grantee shall file with the Secretary of the Company on such form as may be prescribed by the Company, a designation of one or more beneficiaries and, if desired, one or more contingent beneficiaries (each referred to herein as a “Beneficiary”) to whom shares of Common Stock otherwise due the Grantee under the terms of this Agreement shall be distributed in the event of the death of the Grantee. The Grantee shall have the right to change the Beneficiary or Beneficiaries from time to time; provided, however, that any change shall not become effective until received in writing by the Secretary of the

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Company. If any designated Beneficiary survives the Grantee but dies after the Grantee’s death, any remaining benefits due such deceased Beneficiary under this Agreement shall be distributed to the personal representative or executor of the deceased Beneficiary’s estate. If there is no effective Beneficiary designation on file at the time of the Grantee’s death, or if the designated Beneficiary or Beneficiaries have all predeceased such Grantee, the payment of any remaining benefits under this Agreement shall be made to the personal representative or executor of the Grantee’s estate. If one or more but not all the Beneficiaries have predeceased such Grantee, the benefits under this Agreement shall be paid according to the Grantee’s instructions in his designation of Beneficiaries. If the Grantee has not given instructions, or if the instructions are not clear, the benefits under this Agreement which would have been paid to the deceased Beneficiary or Beneficiaries will be paid to the personal representative or executor of Grantee’s estate.

5. Nonalienation of Benefits. Except as contemplated by Section 4 above, no right or benefit under this Agreement shall be subject to transfer, anticipation, alienation, sale, assignment, pledge, encumbrance or charge, whether voluntary, involuntary or by operation of law, and any attempt to transfer, anticipate, alienate, sell, assign, pledge, encumber or charge the same shall be void. No right or benefit hereunder shall in any manner be liable for or subject to any debts, contracts, liabilities or torts of the person entitled to such benefits. If the Grantee or the Grantee’s Beneficiary hereunder shall become bankrupt or attempt to transfer, anticipate, alienate, assign, sell, pledge, encumber or charge any right or benefit hereunder, other than as contemplated by Section 4 above, or if any creditor shall attempt to subject the same to a writ of garnishment, attachment, execution, sequestration or any other form of process or involuntary lien or seizure, then such right or benefit shall cease and terminate.

6. Prerequisites to Benefits. Neither the Grantee, nor any person claiming through the Grantee, shall have any right or interest in Restricted Stock Units awarded hereunder or the shares of Common Stock related thereto, unless and until all the terms, conditions and provisions of this Agreement and the Plan which affect the Grantee or such other person shall have been complied with as specified herein.

7. Payment. Upon satisfaction of all the terms, conditions and provisions of this Agreement and the Plan, a Restricted Stock Unit credited to the Grantee’s account shall be payable to the Grantee in the form of one share of Common Stock.

8. Restrictions on Delivery of Shares. The Company shall not be obligated to deliver any shares of Common Stock if counsel to the Company determines that such issuance or delivery would violate any applicable law or any rule or regulation of any governmental authority or any rule or regulation of, or agreement of the Company with, any securities exchange or association upon which the Common Stock is listed or quoted. If necessary to comply with any such law, rule, regulation or agreement, the Company shall in no event be obligated to take any affirmative action in order to cause the delivery of shares of Common Stock.

9. Rights as a Stockholder. The Grantee (or Beneficiary) shall have no rights as a stockholder with respect to the shares of Common Stock represented by the Restricted Stock Units unless and until all the terms, conditions and provisions of this Agreement and the

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Plan which affect the Grantee or such other person shall have been complied with as specified herein, and certificates evidencing such shares are delivered to the Grantee pursuant to Section 7 hereof.

10. Adjustments. As provided in Paragraph 15 (Adjustments) of the Plan, certain adjustments may be made to the Restricted Stock Units upon the occurrence of events or circumstances described in Paragraph 15 of the Plan.

11. Notice. Unless the Company notifies the Grantee in writing of a different procedure, any notice or other communication to the Company with respect to this Agreement shall be in writing and shall be:

Cabot Oil & Gas Corporation

c/o Corporate Secretary

1200 Enclave Parkway

Houston, Texas 77077

or

Cabot Oil & Gas Corporation

c/o Corporate Secretary

1200 Enclave Parkway

Houston, Texas 77077

Any notice or other communication to the Grantee with respect to this Agreement shall be in writing and shall be delivered personally, or shall be sent by first class mail, postage prepaid, to Grantee’s address as listed in the records of the Company on the Grant Date, unless the Company has received written notification from the Grantee of a change of address.

12. Amendment. Without the consent of the Grantee, this Agreement may be amended or supplemented (i) to cure any ambiguity or to correct or supplement any provision herein which may be defective or inconsistent with any other provision herein, or (ii) to add to the covenants and agreements of the Company for the benefit of Grantee or to add to the rights of the Grantee or to surrender any right or power reserved to or conferred upon the Company in this Agreement, subject, however, to any required approval of the Company’s stockholders and, provided, in each case, that such changes or corrections shall not adversely affect the rights of Grantee with respect to the Award evidenced hereby without the Grantee’s consent, or (iii) to make such other changes as the Company, upon advice of counsel, determines are necessary or advisable because of the adoption or promulgation of, or change in or of the interpretation of, any law or governmental rule or regulation, including any applicable federal or state securities laws.

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13. Grantee Service. Nothing contained in this Agreement, and no action of the Company or the Committee with respect hereto, shall confer or be construed to confer on the Grantee any right to continue as a director of the Company or any Subsidiary.

14. Governing Law. This Agreement shall be governed by, and construed in accordance with, the internal laws of the State of Delaware.

15. Construction. References in this Agreement to “this Agreement” and the words “herein,” “hereof,” “hereunder” and similar terms include all Exhibits and Schedules appended hereto, including the Plan. This Agreement is entered into, and the Award evidenced hereby is granted, pursuant to the Plan. The headings of the Sections of this Agreement have been included for convenience of reference only, are not to be considered a part hereof and shall in no way modify or restrict any of the terms or provisions hereof.

16. Relationship to the Plan. In addition to the terms and conditions described in this Agreement, grants of Restricted Stock are subject to all other applicable provisions of the Plan. The decisions of the Committee with respect to questions arising as to the interpretation of the Plan, or this Agreement and as to finding of fact, shall be final, conclusive and binding.

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