UNION DRILLING, INC. RESTRICTED STOCK UNIT AGREEMENT

Exhibit 10.2

UNION DRILLING, INC.

RESTRICTED STOCK UNIT AGREEMENT

This Restricted Stock Unit Agreement (“Agreement”) is dated as of June 10, 2008 (the “Grant Date”), between Union Drilling, Inc., a Delaware corporation (the “Company”) and Christopher D. Strong (the “Grantee”).

WHEREAS, the Company has adopted, and its stockholders have approved, the Amended and Restated 2005 Stock Incentive Plan (the “Plan”), pursuant to which the Company may grant Restricted Stock Units (“RSUs”), relating to shares of its Common Stock, $0.01 par value per share (the “Common Stock”); and

WHEREAS, the Company desires to grant to the Grantee the number of RSUs provided for herein so as to encourage Grantee’s efforts toward the continuing success of the Company.

NOW, THEREFORE, in consideration of the recitals and the mutual agreements herein contained, the parties hereto agree as follows. Capitalized terms not otherwise defined in this Agreement shall have the meanings specified in the Plan.

Section 1. Grant of Restricted Stock Unit Award.

(a) Grant of Restricted Stock Unit. The Company hereby grants to the Grantee 200,000 Restricted Stock Units on the terms and conditions set forth in this Agreement, and as otherwise provided in the Plan, and based upon Grantee’s satisfaction of the vesting criteria set forth in Section 2(b) below and, if applicable, the performance criteria set forth in Exhibit A hereto.

(b) Incorporation of Plan. The RSUs granted under this Agreement and the provisions of this Agreement are subject to the provisions of the Plan, the terms of which are incorporated herein by this reference. In the event of any inconsistency between the provisions of this Agreement and the Plan, the Plan shall govern. Capitalized terms used herein without definition shall have the meanings assigned to them in the Plan. The Committee shall have final authority to interpret and construe the Plan and this Agreement and to make any and all determinations thereunder, and its decision shall be binding and conclusive upon the Grantee and his/her legal representative in respect of any questions arising under the Plan or this Agreement.

Section 2. Terms and Conditions of Award.

The grant of RSUs provided in Section 1(a) shall be subject to the following terms, conditions and restrictions:

(a) Restrictions. Neither any of the RSUs subject to this Award, nor any interest therein, may be sold, assigned, transferred, pledged, hypothecated or otherwise disposed of, prior

to the vesting and settlement thereof in accordance with the terms of this Award. Any attempt to transfer, assign, pledge, or otherwise dispose of this Award or any right or privilege conferred by this Agreement, contrary to the provisions hereof, shall be null and void.

(b) Vesting.

(i) Provided that (A) the performance-based vesting conditions set forth on Exhibit A are satisfied on or as of the end of any fiscal quarter prior to the relevant vesting date identified in this Section and (B) the Grantee remains in continuous service as an Employee, Officer or Director from the Grant Date to the relevant vesting date, and unless vesting occurs earlier pursuant to subsections (ii) and (iii) below, 25% of the RSUs (rounded to the nearest whole unit) granted hereunder shall vest and become nonforfeitable on each of the fifth anniversary and sixth anniversary of the Grant Date and the remaining 50% of the RSUs granted hereunder shall vest and become nonforfeitable on the seventh anniversary of the Grant Date.

(ii) Notwithstanding subsection (i) above, vesting of any then unvested RSUs shall occur on the first to occur of the following dates without regard to the conditions set forth on Exhibit A; provided the Grantee continues to serve as an Employee, Officer or Director from the Grant Date to such date that:

(A) the Grantee terminates serving as an Employee, Officer or Director due to Disability; or

(B) the Grantee terminates serving as an Employee, Officer or Director due to death.

(iii) The Committee may in its discretion accelerate the vesting of all or any portion of any outstanding unvested RSUs prior to the expiration of the periods provided in subsection (b)(i) above without regard to the conditions set forth on Exhibit A.

(iv) All vested RSUs shall be settled or paid in accordance with Section 2(e).

(c) Cessation of Service. In the event that the Grantee’s service as an Employee, Officer or Director ceases prior to vesting of any portion of the RSUs granted hereunder, except if such services cease for the reasons described in Sections 2(b)(ii)(A) and 2(b)(ii)(B), all unvested RSUs held by the Grantee shall be immediately forfeited as of the date of such cessation of service unless the Committee shall determine otherwise. RSUs forfeited pursuant to this Section 2(c) shall be forfeited without payment of any consideration by the Company, and neither the Grantee nor any of the Grantee’s successors, heirs, assigns or personal representatives shall thereafter have any further rights or interests in such forfeited RSUs.

(d) Income Taxes. The Grantee shall pay to the Company promptly upon request, and in any event at the time the Grantee recognizes taxable income in respect of the RSUs, an amount equal to the taxes the Company determines it is required to withhold under applicable tax laws with respect to the RSUs. Such payment shall be made in the form of cash, shares of Common Stock, which may be withheld from the shares of Common Stock otherwise deliverable upon settlement of this Award, or in a combination of such methods.

2

(e) Settlement. Any RSUs becoming nonforfeitable in accordance with Sections 2(b) or 2(c) above shall be settled promptly thereafter, but in no event later than 75 days after the end of the calendar year in which the applicable vesting date occurs. Payment shall be made in cash or shares of Common Stock, or any combination thereof, as determined by the Committee in its sole discretion.

If at the time of any settlement of RSUs, the tax deduction normally available to the Company as a result of the settlement of RSUs in accordance with this Section 2(e) would be limited by Section 162(m) of the Code, such RSUs shall not be settled on such date, but shall be settled in the earliest tax year in which the Committee determines that a tax deduction arising from such settlement would not be limited by Section 162(m). In applying the deduction limit of Section 162(m), the Committee shall first apply any limitation of deductibility, and settlement, in reverse order to the date on which the RSU first became vested, i.e. RSUs more recently vested shall be considered deductible before RSUs vested in earlier periods.

(f) Legal Compliance. Shares of Common Stock delivered pursuant to Section 2(e) may, at the election of the Company, be either authorized and unissued shares, or shares previously issued and reacquired by the Company. The Company shall not be required to issue or deliver any certificates for such shares of Common Stock prior to: (i) the obtaining of any legal opinion or related documentation, or the approval from any governmental agency, which the Committee shall, in its sole discretion, determine to be necessary or advisable; (ii) the listing of such shares on any Exchange on which the Stock may then be listed; (iii) the completion of any registration or other qualification of such shares under any state or federal law or ruling or regulation of any governmental body which the Committee shall, in its sole discretion, determine to be necessary or advisable; or (iv) the determination by the Committee that the Grantee has tendered to the Company any tax owed when the Company has a legal liability to satisfy such tax. In addition, if the Common Stock is not registered under the Securities Act of 1933, as amended, the Company may require the Grantee to represent in writing that the shares being acquired are for investment and not with a view to distribution; may mark the certificate for the shares with a legend restricting transfer; and may issue stop transfer orders relating to such certificate to the Company’s transfer agent.

(g) Change of Control. Notwithstanding anything in this Agreement to the contrary, without regard to the conditions set forth in Exhibit A, all of the RSUs granted hereunder shall become immediately vested and nonforfeitable in the event that, following a Change of Control of the Company, Grantee’s employment with the Company is terminated by the Company without Cause or by Grantee for Good Reason.

As used in this Agreement, a “Change of Control of the Company” shall be deemed to have occurred if and only if after the Grant Date any person or group of affiliated persons, other than the current stockholders of the Company or their affiliates, is or becomes the beneficial owner, directly or indirectly, of securities of the Company representing more than 50% of the combined voting power of the Company’s then outstanding securities.

3

As used in this Agreement, the term “Cause” shall mean and include Grantee’s (i) chronic alcoholism or controlled substance abuse, (ii) commission of an act of fraud or dishonesty with respect to the Company or its subsidiaries, as determined in the sole discretion of the Board; (iii) knowing and material failure to comply with material applicable laws, regulations or Company policies relating to the business of the Company or its subsidiaries; (iv) material and continuing failure to perform (as opposed to unsatisfactory performance) his duties as an officer and employee of the Company which is not corrected within 10 days after receipt of written notice from the Company, except, in each case, where such failure or breach is caused by his illness or other similar incapacity or Disability; or (v) conviction of (or pleading guilty or nolo contendere to) a felony.

As used in this Agreement, the term “Good Reason” shall mean and include (i) that, upon the expiration of 180 days following the date on which the Change of Control of the Company shall be deemed to have been consummated, there has been a failure to elect or reelect or to appoint or reappoint, either with the Company or any successor entity to the Company, Grantee to the chief executive officer position held by Grantee immediately prior to the Change of Control of the Company, (ii) a change by the Company (or any successor entity) of Grantee’s functions, duties or responsibilities that materially reduce Grantee’s functions, duties or responsibilities as in effect immediately prior to the Change of Control of the Company; or (iii) a reduction in Grantee’s base salary, other than as a result of any reduction in base salary made on a basis substantially proportionate to reductions in salary made to other senior executives of the Company (or any successor entity).

Section 3. Miscellaneous.

(a) Notices. All notices under this Agreement to the Company must be delivered personally or mailed to the Company at Union Drilling, Inc., 4055 International Plaza, Suite 610, Fort Worth, Texas 76109, Attention: General Counsel. The Company’s address may be changed at any time by written notice of such change to the Grantee. Also, all notices under this Agreement to the Grantee will be delivered personally or mailed to the Grantee at his or her address as shown from time to time in the Company’s records.

(b) No Right to Continued Service. Nothing in the Plan or in this Agreement shall (i) confer upon the Grantee any right to continue to serve as a Director, Officer or Employee, or shall it interfere in any way with the right of any Participating Company to terminate Grantee’s employment at any time, or (ii) interfere with or restrict in any way the right of the stockholders of the Company, which is hereby expressly reserved, to remove the Grantee as a Director at any time in accordance with applicable law or the Company’s by-laws.

(c) Bound by Plan. By signing this Agreement, the Grantee acknowledges that he/she has received a copy of the Plan and has had an opportunity to review the Plan and agrees to be bound by all the terms and provisions of the Plan.

(d) Successors. The terms of this Agreement shall be binding upon and inure to the benefit of the Company, its successors and assigns, and of the Grantee and the beneficiaries, executors, administrators, heirs and successors of the Grantee.

4

(e) Invalid Provision. If any provision of this Agreement is held to be illegal, invalid, or unenforceable under any applicable laws, the legality, validity, and enforceability of the remaining provisions of this Agreement shall not be affected thereby, and in lieu of such illegal, invalid, or unenforceable provision, there shall be added automatically as a part of this Agreement a provision as similar in terms to such illegal, invalid, or unenforceable provision as may be possible and be legal, valid and enforceable.

(f) Modifications. Any amendment to the Plan shall be deemed to be an amendment to this Agreement to the extent that the amendment is applicable hereto; provided that no amendment shall adversely affect the Grantee’s rights under this Agreement without the Grantee’s consent. Except as provided in the immediately preceding sentence, the terms and conditions of this Agreement may not be modified, amended or waived, except by an instrument in writing signed by the Grantee and a duly authorized executive officer of the Company.

(g) Entire Agreement. This Agreement and the Plan contain the entire agreement and understanding of the parties hereto with respect to the subject matter contained herein and therein and supersede all prior communications, representations and negotiations in respect thereto.

(h) Governing Law. This Agreement and the rights of the Grantee hereunder shall be construed and determined in accordance with the laws of the State of Texas, without regard to the conflicts of laws principles thereof. Venue for any dispute arising hereunder shall lie exclusively in the state and/or federal courts of Tarrant County, Texas and the Northern District of Texas, Fort Worth Division, respectively.

(i) Headings. The headings of the Sections hereof are provided for convenience only and are not to serve as a basis for interpretation or construction, and shall not constitute a part of this Agreement.

(j) Counterparts. This Agreement may be executed in counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

(k) Satisfaction of Claims. Any payment or any issuance or transfer of shares of Common Stock upon lapse of the forfeiture restrictions hereunder to the Grantee or the Grantee’s legal representative, heir, legatee or distributee, in accordance with the provisions hereof, shall, to the extent thereof, be in full satisfaction of all claims of such person hereunder. The Committee may require the Grantee or the Grantee’s legal representative, heir, legatee or distributee, as a condition precedent to such payment, to execute a release and receipt therefor in such form as it shall determine.

(l) IF THIS AGREEMENT IS NOT SIGNED AND RETURNED TO THE OFFICES OF THE COMPANY WITHIN 30 DAYS AFTER THE GRANT DATE, THIS AGREEMENT AND THE RESTRICTED STOCK UNIT AWARD PROVIDED FOR HEREIN SHALL BE NULL AND VOID.

5

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first above written.

The undersigned hereby acknowledges receipt of an executed original of this Agreement and a copy of the Plan, and accepts the award of Restricted Stock Units granted thereunder on the terms and conditions set forth herein and in the Plan.

6

Exhibit A

Performance-Based Vesting Criteria

The following performance-based vesting criteria shall apply to the Grantee’s Restricted Stock Units and, upon achievement of such criteria below on or as of the end of any fiscal quarter prior to a vesting date specified in Section 2(b)(i) of the Agreement, the applicable number of RSUs designated shall be conditionally vested, subject to the Grantee’s satisfaction of the time-based vesting conditions described in Section 2(b)(i). These conditions shall not apply to vesting of RSUs pursuant to Sections 2(b)(ii), 2(b)(iii) or 2(g) of the Agreement.

RSUs conditionally vesting in accordance with the foregoing shall unconditionally vest and become nonforfeitable upon satisfaction of the time-based vesting requirements described in Section 2(b)(i) of the Agreement.

7