Exhibit 10.10.1

RESTRICTED UNIT AWARD AGREEMENT FOR

CHESAPEAKE MIDSTREAM

LONG-TERM INCENTIVE PLAN

THIS RESTRICTED UNIT AWARD AGREEMENT (the “Agreement”) entered into as of the grant date set forth on the attached Notice of Grant of Award and Award Agreement (the “Notice”), by and between Chesapeake Midstream GP, L.L.C. (the “General Partner”), the general partner of Chesapeake Midstream Partners, L.P. (the “Partnership”), and the participant named on the Notice (the “Participant”);

W I T N E S S E T H:

WHEREAS, the General Partner has adopted the Chesapeake Midstream Long-Term Incentive Plan (the “Plan”); and

WHEREAS, the Participant is an Employee (as defined in the Plan), and it is important to the General Partner that the Participant be encouraged to remain an Employee;

NOW, THEREFORE, in consideration of the premises and the mutual promises and covenants herein contained, the Participant and the General Partner agree as follows:

1. The Plan. The Plan, a copy of which has been made available to the Participant, is incorporated by reference herein and made a part hereof for all purposes, and when taken with this Agreement (which includes the Notice) shall govern the rights of the Participant and the General Partner with respect to the Award (as defined below). In the event of any conflict between the terms of this Agreement and the Plan, which is incorporated herein by reference as a part of this Agreement, the terms of the Plan shall control. Any capitalized terms used but not defined in this Agreement have the same meanings given to them in the Plan.

2. Grant of Award. The General Partner hereby grants to the Participant an award (the “Award”) of notional Units of the Partnership (“Restricted Units”), as set forth on the Notice, on the terms and conditions set forth herein, including in the Notice, and in the Plan.

3. Terms of Award.

(a) Service Vesting. The Restricted Units will vest based on the Participant’s continuous employment with the General Partner, the Partnership, Chesapeake Midstream Management, L.L.C. (“CMM”) or any of their Affiliates in accordance with the vesting schedule set forth on the Notice. For purposes of this Agreement, “employment” means being an Employee, Consultant or Director, of the General Partner, the Partnership, CMM or any of their Affiliates and a change in status between being an Employee, Consultant or Director shall not constitute a termination of employment. Notwithstanding anything herein to the contrary, a termination of employment must also be a “separation from service” for purposes of Section 409A of the Code.

(b) Forfeiture. In the event the Participant’s employment with the General Partner, the Partnership, CMM and their Affiliates terminates prior to all Restricted Units becoming vested pursuant to paragraph 3(a) or 3(d), any Restricted Units that have not yet vested shall be forfeited automatically on such termination of employment and the Participant shall have no further interest therein of any kind whatsoever. However, the Committee may, in its sole discretion, accelerate the vesting of all or part of the then balance of this Award in the event of the Participant’s death, Disability or termination due to special circumstances (as determined by the Committee in its sole discretion).

(c) Distribution Equivalent Rights (“DERs”). The General Partner shall establish, with respect to each Restricted Unit granted, a separate bookkeeping account for such Restricted Unit (a “DER Account”), which shall be credited (without interest) with an amount equal to any cash distributions made by the Partnership with respect to a Unit during the period such Restricted Unit remains credited to the Participant. Upon the vesting of a Restricted Unit, the DER Account with respect to such vested Restricted Unit shall also become vested. Similarly, upon the forfeiture of a Restricted Unit, the DER Account with respect to such forfeited Restricted Unit shall also be forfeited.

(d) Change of Control Vesting. Upon a Change of Control, the unvested Restricted Units and unvested DER Accounts then credited to the Participant pursuant to this Agreement automatically shall vest in full.

4. Payment of Vested Restricted Units and DER Accounts.

(a) Restricted Units. Subject to Section 5 below, as soon as reasonably practical, but not later than 60 days, following the date Restricted Units vest, the General Partner shall cause to be delivered (whether in certificate or electronic form, in the Committee’s discretion) to the Participant that number of Units equal to the number of Restricted Units then vesting.

(b) DER Accounts. Subject to Section 5 below, as soon as reasonably practical, but not later than 60 days, following the date a Restricted Unit vests, the General Partner shall cause to be paid to the Participant an amount of cash equal to the amount then credited to the DER Account maintained with respect to such Restricted Unit.

5. Withholding of Taxes. If the grant or payment of a Restricted Unit, or the payment of cash with respect to a DER Account, results in the receipt of compensation by the Participant with respect to which the General Partner or an Affiliate has a tax withholding obligation pursuant to applicable law, the General Partner or such Affiliate shall withhold (or “net”) (i) from that number of Units otherwise deliverable to the Participant and (ii) from the amount of cash otherwise payable to the Participant, such number of Units with respect to (i) above and amount of cash with respect to (ii) above as the General Partner or such Affiliate requires to meet its tax withholding obligations under such applicable law; provided, however, that the Committee in its discretion may permit the Participant to deliver cash or other property to the General Partner or an Affiliate in satisfaction of such tax withholding obligations under applicable law. No delivery of a Unit with respect to a vested Restricted Unit or payment of cash with respect to a vested DER Account shall be made pursuant to this Agreement until the applicable tax withholding requirements of the General Partner or the Affiliate with respect to such event have been satisfied in full.

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6. Nontransferability of Award. The Participant shall not have the right to sell, assign, transfer, convey, dispose, pledge, hypothecate, burden, encumber or charge any Restricted Unit or DER Account or any interest therein in any manner whatsoever, (whether by operation of law or otherwise), other than by will or the laws of descent and distribution and shall not be subject to execution, attachment, or similar process. Any attempted assignment, transfer, pledge, hypothecation or other disposition of a Restricted Unit or DER Account contrary to the provisions hereof shall be null and void and without effect.

7. Amendments. This Award Agreement may be amended by a written agreement signed by the General Partner and the Participant; provided, however, that, subject to the provisions of the Plan, the Committee may modify the terms of this Award Agreement without the consent of the Participant in any manner that is not materially adverse to the vested rights or benefits of the Participant.

8. Securities Law Restrictions. This Award shall be vested and be paid only in compliance with the Securities Act of 1933, as amended (the “Act”), and any other applicable securities law, or pursuant to an exemption therefrom. If deemed necessary by the General Partner to comply with the Act or any applicable laws or regulations relating to the sale of securities, the Participant at the time of vesting and as a condition imposed by the General Partner, shall represent, warrant and agree that Units of the Partnership acquired pursuant to the vesting of the Award are being acquired for investment and not with any present intention to resell the same and without a view to distribution, and the Participant shall, upon the request of the General Partner, execute and deliver to the General Partner an agreement to such a fact. The Participant acknowledges that any unit certificate representing Units of the Partnership acquired under such circumstances will be issued with a restricted securities legend.

9. Notices. All notices or other communications relating to the Plan and this Agreement as it relates to the Participant shall be in writing, shall be deemed to have been made (a) if personally delivered in return for a receipt, (b) if mailed, by regular U.S. mail, postage prepaid, by the General Partner to the Participant at his last known address evidenced on the General Partner’s or its Affiliate’s payroll records or (c) if provided electronically, provided to the Participant at his e-mail address specified in the General Partner’s or its Affiliate’s records or as other specified pursuant to and in accordance with the Committee’s applicable administrative procedures.

10. Binding Effect and Governing Law. This Agreement shall be (i) binding upon and inure to the benefit of the parties hereto and their respective heirs, successors and assigns except as may be limited by the Plan and (ii) governed and construed under the laws of the State of Oklahoma, without regard to conflicts of laws principles thereof.

11. Entire Agreement. Except as may be specifically provided in a written employment or severance agreement between Participant and Participant’s employer, this Agreement, including the Notice and subject to the Plan, constitutes the entire agreement of all parties hereto with regard to the subject matter hereof, and contains all the covenants, promises,

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representations, warranties and agreements between the parties with respect to the Restricted Units and DERs granted hereby. Without limiting the scope of the preceding sentence, all prior understandings and agreements, if any, among the parties hereto relating to the subject matter hereof are hereby null and void and of no further force and effect. In making this grant, and taking all other actions under the Plan and this Agreement, the General Partner is acting on its behalf and also on behalf of CMM, which is deemed to be a “party” to this Agreement.

12. Captions. The captions of specific provisions of this Agreement are for convenience and reference only, and in no way define, describe, extend or limit the scope of this Agreement or the intent of any provision hereof.

13. Counterparts. This Agreement may be executed in any number of identical counterparts, each of which shall be deemed an original for all purposes, but all of which taken together shall form but one agreement.

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Notice of Grant of Award

and Award Agreement

under the Chesapeake Midstream

Long-Term Incentive Plan

Effective as of [date] (the “Grant Date”), you have been granted an award of Restricted Units under the Plan with respect to Units of the Partnership. Each Restricted Unit represents one notional Unit of the Partnership. The Restricted Units granted hereby are restricted until the vesting date(s) shown below.

The current total value of the Award is $                    , based on the Fair Market Value of a Unit on the Grant Date.

The Award will become vested in increments on the date(s) shown.

By your signature and the General Partner’s signature below, you and the General Partner agree that this Award is granted under and governed by the terms and conditions of the Plan and the Award Agreement.