Exhibit (a)(1)(D)

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

Bronco Drilling Company, Inc.

at

$11.00 Per Share

by

Nomac Acquisition, Inc.

an indirect wholly owned subsidiary of

Chesapeake Energy Corporation

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF MONDAY, MAY 23, 2011, UNLESS THE OFFER IS EXTENDED.

April 26, 2011

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

Nomac Acquisition, Inc., a Delaware corporation (“Purchaser”) and an indirect wholly owned subsidiary of Chesapeake Energy Corporation, an Oklahoma corporation (“Chesapeake”), is making an offer to purchase all outstanding shares of common stock, par value $0.01 per share, of Bronco Drilling Company, Inc. (the “Bronco shares”), a Delaware corporation (“Bronco”), at a purchase price of $11.00 per share in cash, without interest, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated April 26, 2011 (the “Offer to Purchase”), and in the related Letter of Transmittal (which, together with any amendments or supplements thereto, collectively constitute the “offer”) enclosed herewith.

Please furnish copies of the enclosed materials to those of your clients for whose accounts you hold Bronco shares registered in your name or in the name of your nominee.

Enclosed herewith for your information and forwarding to your clients are copies of the following documents:

1. Offer to Purchase dated April 26, 2011.

2. The Letter of Transmittal for your use in accepting the offer and tendering Bronco shares and for the information of your clients.

3. Notice of Guaranteed Delivery to be used to accept the offer if certificates for Bronco shares and all other required documents cannot be delivered to Computershare Trust Company, N.A. (the “Depositary”), or if the procedures for book-entry transfer cannot be completed, by the expiration date of the offer.

4. A letter that may be sent to your clients for whose accounts you hold Bronco shares registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the offer.

5. Bronco’s Solicitation/Recommendation Statement on Schedule 14D-9.

6. Internal Revenue Service Form W-9.

7. Return envelope addressed to the Depositary.

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YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF MONDAY, MAY 23, 2011, UNLESS THE OFFER IS EXTENDED.

This offer is being made pursuant to an Agreement and Plan of Merger, dated as of April 14, 2011 (the “merger agreement”), by and among Chesapeake, Purchaser and Bronco. The merger agreement provides, among other things, that, on the terms and subject to the terms set forth in the merger agreement, after consummation of the offer, Purchaser will merge with and into Bronco (the “merger”), with Bronco continuing as the surviving corporation (the “surviving corporation”) and an indirect wholly owned subsidiary of Chesapeake. At the effective time of the merger (the “merger effective time”), each outstanding Bronco share (other than any Bronco shares held by Chesapeake, Purchaser, Bronco or any wholly owned subsidiary of Bronco or Chesapeake, and any Bronco shares held by stockholders who validly exercise their appraisal rights in connection with the merger) will be cancelled and extinguished and automatically converted into the right to receive the price per Bronco share paid in the offer, without interest.

The Board of Directors of Bronco has unanimously (i) declared that the merger agreement and the transactions contemplated by the merger agreement, including the offer and the merger, are fair to, advisable and in the best interests of Bronco and its stockholders and (ii) approved and declared advisable the merger agreement. THE BOARD OF DIRECTORS OF BRONCO RECOMMENDS THAT BRONCO STOCKHOLDERS ACCEPT THE OFFER AND TENDER THEIR BRONCO SHARES INTO THE OFFER.

There is no financing condition to the offer. The offer is conditioned upon, among other things, (1) there being validly tendered in accordance with the terms of the offer, prior to the expiration date of the offer (as it may be extended from time to time) and not withdrawn, at least a majority of the total number of outstanding shares of Bronco common stock, on a fully diluted basis (which assumes conversion or exercise of all derivative securities of Bronco, regardless of the conversion or exercise price or other terms and conditions thereof) (excluding from the number of tendered Bronco shares, but not from the outstanding Bronco shares, Bronco shares tendered pursuant to the guaranteed delivery procedures that have not yet been delivered in settlement or satisfaction of such guarantee), (2) the expiration or termination of the applicable waiting period (and any extension thereof) under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended (the “Antitrust Condition”), and (3) there having not been imposed, in connection with satisfying the Antitrust Condition, any obligation of Chesapeake or any of its subsidiaries or affiliates to accept, commit to or effect the sale, divestiture or disposition of any assets or businesses of Chesapeake or Bronco or any of their respective subsidiaries or affiliates, or otherwise take or commit to take actions that after the closing of the transaction would limit Chesapeake’s freedom of action with respect to, or ability to retain, any portion of Chesapeake’s, Bronco’s or any of their subsidiaries’ or affiliates’ business or assets. A summary of the principal terms of the offer is described in the Offer to Purchase.

Upon the terms and subject to the conditions of the offer (including, if the offer is extended or amended, the terms and conditions of any such extension or amendment), Purchaser will be deemed to have accepted for payment, and will pay for, all Bronco shares validly tendered and not properly withdrawn by the expiration date of the offer if and when Purchaser gives oral or written notice to the Depositary of Purchaser’s acceptance of the tenders of such Bronco shares for payment pursuant to the offer. In all cases, Purchaser will pay for Bronco shares accepted for payment pursuant to the offer only after timely receipt by the Depositary of (a) certificates representing such Bronco shares or timely confirmation of a book-entry transfer of such Bronco shares into the Depositary’s account at the Book-Entry Transfer Facility (as defined in the Offer to Purchase) (“Book-Entry Confirmation”) pursuant to the procedures set forth in Section 3 of the Offer to Purchase, (b) a properly completed and duly executed Letter of Transmittal with all required signature guarantees or, in the case of a book-entry transfer, an Agent’s Message (as defined in Section 3 of the Offer to Purchase) in lieu of the Letter of Transmittal, and (c) any other documents required by the Letter of Transmittal. Accordingly, tendering

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stockholders may be paid at different times depending upon when certificates for Bronco shares or Book-Entry Confirmations with respect to Bronco shares are actually received by the Depositary. Under no circumstances will interest be paid on the consideration paid for Bronco shares pursuant to the offer, regardless of any extension of the offer or any delay in making payment for Bronco shares.

Purchaser is not aware of any jurisdiction where the making of the offer is prohibited by any administrative or judicial action pursuant to any valid state statute. If Purchaser becomes aware of any valid state statute prohibiting the making of the offer or the acceptance of the Bronco shares, Purchaser will make a good faith effort to comply with that state statute. If, after a good faith effort, Purchaser cannot comply with the state statute, Purchaser will not make the offer to, nor will Purchaser accept tenders from or on behalf of, the holders of Bronco shares in that state. In any jurisdiction where the securities, blue sky or other laws require the offer to be made by a licensed broker or dealer, the offer will be deemed to be made on behalf of Purchaser or by one or more registered brokers or dealers licensed under the laws of such jurisdiction.

Purchaser will not pay any fees or commissions to any broker, dealer or other person (other than MacKenzie Partners, Inc. (the “Information Agent”) and the Depositary as described in the Offer to Purchase) for soliciting tenders of Bronco shares pursuant to the offer. Purchaser will, however, upon request, reimburse brokers, dealers, commercial banks and trust companies for customary mailing and handling costs incurred by them in forwarding the enclosed materials to their customers.

Purchaser will pay all stock transfer taxes applicable to its purchase of Bronco shares pursuant to the offer, subject to Instruction 6 of the Letter of Transmittal.

If holders of Bronco shares wish to tender, but it is impracticable for them to forward their certificates or other required documents or to complete the procedures for delivery by book-entry transfer prior to the expiration of the offer, a tender may be effected by following the guaranteed delivery procedures described in Section 3 of the Offer to Purchase.

Any inquiries you may have with respect to the offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the Information Agent at its address and telephone numbers set forth on the back cover of the Offer to Purchase.

Very truly yours,

Chesapeake Energy Corporation

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU THE AGENT OF CHESAPEAKE, PURCHASER, BRONCO, THE INFORMATION AGENT OR THE DEPOSITARY, OR ANY AFFILIATE OF ANY OF THEM OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN.

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