Exhibit (a)(5)(A)

This announcement is neither an offer to purchase nor a solicitation of an offer to sell Bronco shares (as defined below). The offer (as defined below) is made solely by the Offer to Purchase dated April 26, 2011 and the related Letter of Transmittal and any amendments or supplements thereto. Purchaser (as defined below) 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, the offer will not be made to, nor will tenders be accepted 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 by one or more registered brokers or dealers licensed under the laws of such jurisdiction.

Notice of Offer to Purchase

All Outstanding Shares of Common Stock

of

Bronco Drilling Company, Inc.

at

$11.00 Per Share

Pursuant to the Offer to Purchase Dated April 26, 2011

by

Nomac Acquisition, Inc.

an indirect wholly owned subsidiary of

Chesapeake Energy Corporation

Nomac Acquisition, Inc., a Delaware corporation (“Purchaser”) and an indirect wholly owned subsidiary of Chesapeake Energy Corporation, an Oklahoma corporation (“Chesapeake”), is offering to purchase all outstanding shares of common stock, par value $0.01 per share (the “Bronco shares”), of Bronco Drilling Company, Inc., a Delaware corporation (“Bronco”), for $11.00 per Bronco share in cash, without interest (the “offer price”), upon the terms and subject to the conditions set forth in the Offer to Purchase and the related Letter of Transmittal (collectively, the “offer”). All references to the Offer to Purchase, the Letter of Transmittal and the offer include any amendments or supplements to the Offer to Purchase and the Letter of Transmittal, respectively.

Tendering stockholders whose Bronco shares are registered in their names and who tender directly to Computershare Trust Company, N.A. (the “Depositary”) will not be charged brokerage fees or commissions or, except as set forth in Instruction 6 of the Letter of Transmittal, transfer taxes on the purchase of Bronco shares pursuant to the offer. Tendering stockholders, whose Bronco shares are registered in the name of their broker, bank or other nominee should consult such nominee to determine if any fees may apply. Following the consummation of the offer, and subject to the conditions described in the Offer to Purchase, Purchaser intends to effect the merger (as defined below).

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.

The offer is conditioned upon there being validly tendered and not properly withdrawn prior to the expiration of the offer that number of Bronco shares that represents at least a majority of the total number of outstanding Bronco shares on a fully diluted basis (which assumes conversion or exercise of all derivative

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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). The offer is also subject to the satisfaction of additional conditions set forth in the Offer to Purchase, including the expiration or termination of the applicable waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended. A summary of the principal terms of the offer appears in the Offer to Purchase.

The offer is being made pursuant to an Agreement and Plan of Merger, dated as of April 14, 2011, among Chesapeake, Purchaser and Bronco (the “merger agreement”). The merger agreement provides, among other things, that after consummation of the offer, Purchaser will merge with and into Bronco (the “merger”), with Bronco continuing as the surviving corporation and an indirect wholly owned subsidiary of Chesapeake. At the effective time of the merger, 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 offer price. The merger agreement is more fully described in Section 12 of the Offer to Purchase.

Bronco’s board of directors 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. BRONCO’S BOARD OF DIRECTORS RECOMMENDS THAT BRONCO STOCKHOLDERS ACCEPT THE OFFER AND TENDER THEIR BRONCO SHARES INTO THE OFFER.

The initial offering period of the offer will expire at 12:00 midnight, New York City time, at the end of Monday, May 23, 2011, unless Purchaser extends the offer. If at the scheduled expiration date of the offer, including following a prior extension, any condition to the offer has not been satisfied or waived, Purchaser is permitted to extend the offer for one or more periods of not more than five business days per period. Purchaser also may, without the consent of Bronco, elect to provide a “subsequent offering period.” A subsequent offering period, if one is provided, will be an additional period of not less than three and no more than 20 business days beginning after we have purchased Bronco shares tendered during the offer.

Any extension, termination or amendment of the offer will be followed as promptly as practicable by public announcement thereof to be made no later than 9:00 a.m., New York City time, on the next business day after the previously scheduled expiration date. During any extension of the offer, all Bronco shares previously tendered and not withdrawn will remain subject to the offer and subject to the rights of a tendering stockholder to withdraw such stockholder’s Bronco shares.

In accordance with Rule 14d-11 under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the merger agreement, Purchaser expressly reserves the right to provide, at its option, a subsequent offering period following the expiration date. If provided, a subsequent offering period will be an additional period of time, following the expiration of the offer and the purchase of Bronco shares in the offer, during which stockholders may tender any Bronco shares not previously tendered in the offer. If a subsequent offering period is made available, (i) it will remain open for such period or periods as we will specify of at least three business days, (ii) Bronco shares may be tendered in the same manner as was applicable to the offer except that any Bronco shares tendered may not be withdrawn, (iii) Purchaser will immediately accept and promptly pay for Bronco shares as they are tendered and (iv) the price per Bronco share will be the same as the offer price. Purchaser may extend any initial subsequent offering period by any period or periods, provided that the aggregate duration of the subsequent offering period (including extensions thereof) is no more than 20 business days. Pursuant to Rule 14d-7(a)(2) under the Exchange Act, withdrawal rights do not apply to Bronco shares tendered during a subsequent offering period. A subsequent offering period, if one is provided, is not an

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extension of the offer, which already would have been completed. For purposes of the offer, a “business day” means any day other than a Saturday, Sunday or other day on which banking institutions are required or authorized by law to be closed in New York, New York or Oklahoma City, Oklahoma and consists of the time period from 12:01 a.m. through 12:00 midnight, New York City time.

Purchaser also reserves the right to waive, in whole or in part, any of the conditions to the offer and to change the offer price; provided that Bronco’s prior written consent is required for Purchaser to (i) reduce the number of Bronco shares subject to the offer, (ii) reduce the offer price, (iii) change or waive the condition to the offer that at least a majority of the total number of outstanding Bronco shares on a fully diluted basis has been validly tendered and not properly withdrawn prior to the expiration of the offer, (iv) add any conditions to the offer in addition to those set forth in Section 14 of the Offer to Purchase, (v) except as described above, extend the expiration date, (vi) change the form of consideration payable in the offer or (vii) amend any term of the offer in a manner adverse to Bronco’s stockholders.

In connection with the execution and delivery of the merger agreement, Chesapeake and Purchaser entered into tender support agreements, dated as of April 14, 2011, with Third Avenue Management LLC, on behalf of its investment advisory clients, and with Inmobiliaria Carso, S.A. de C.V. and Carso Infraestructura y Construcción, S.A.B. de C.V. (the “Supporting Stockholders”). Pursuant to the tender support agreements, the Supporting Stockholders agreed, subject to certain limited specified exceptions, to tender, and not withdraw, all Bronco shares beneficially owned by them (or, in the case of Third Avenue, all of the Bronco shares beneficially owned by its investment advisory clients), or acquired by them (or, in the case of Third Avenue, all of the Bronco shares acquired by its investment advisory clients) after such date. In addition, such stockholders have agreed, subject to certain exceptions, to vote their Bronco shares in favor of the merger and to refrain from disposing of their Bronco shares and soliciting alternative acquisition proposals to the merger. The tender support agreements will terminate upon certain circumstances, including upon termination of the merger agreement. Currently, the Bronco shares subject to the tender support agreements constitute approximately 32% of the outstanding Bronco shares in the offer. See Section 12 of the Offer to Purchase.

In order to take advantage of the offer, a tendering stockholder must either (i) complete and sign the Letter of Transmittal in accordance with the instructions in the Letter of Transmittal, have such stockholder’s signature guaranteed (if required by Instruction 1 to the Letter of Transmittal), mail or deliver the Letter of Transmittal (or a facsimile copy) and any other required documents to the Computershare Trust Company, N.A., the Depositary, and either deliver the certificates representing the tendered Bronco shares along with the Letter of Transmittal to the Depositary or tender such Bronco shares pursuant to the procedures for book-entry transfer set forth in Section 3 of the Offer to Purchase or (ii) request such stockholder’s broker, dealer, commercial bank, trust company or other nominee to effect the transaction. If Bronco shares are registered in the name of a broker, dealer, commercial bank, trust company or other nominee, a tendering stockholder must contact such broker, dealer, commercial bank, trust company or other nominee to tender such Bronco shares. If a tendering stockholder desires to tender Bronco shares, and certificates evidencing such Bronco shares are not immediately available, or if a tendering stockholder cannot comply with the procedures for book-entry transfer described in the Offer to Purchase on a timely basis, or cannot deliver all required documents to the Depositary prior to the expiration of the offer, such tendering stockholder may tender Bronco shares by following the procedures for guaranteed delivery set forth in Section 3 of the Offer to Purchase.

For purposes of the offer, Purchaser will be deemed to have accepted for payment tendered Bronco shares when, as and if Purchaser gives oral or written notice of Purchaser’s acceptance to the Depositary. Purchaser will pay for Bronco shares accepted for payment pursuant to the offer by depositing the purchase price with the Depositary, which will act as agent for tendering stockholders for the purpose of receiving payments from Purchaser and transmitting such payments to tendering stockholders. Under no circumstances will Purchaser pay interest on the consideration paid for Bronco shares pursuant to the offer, regardless of any extension of the offer or any delay in making such payment.

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In all cases (including during any subsequent offering period), Purchaser will pay for Bronco shares accepted for payment pursuant to the offer only after timely receipt by the Depositary of (i) certificates representing such Bronco shares or timely confirmation of the 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) pursuant to the procedures set forth in Section 3 of the Offer to Purchase, (ii) a properly completed and duly executed Letter of Transmittal (or facsimile thereof) 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 (iii) any other documents required by the Letter of Transmittal.

Except as otherwise provided in the Offer to Purchase, tenders of Bronco shares made in the offer are irrevocable. Bronco shares tendered pursuant to the offer may be withdrawn at any time before the expiration date and, unless previously accepted for payment as provided herein, may also be withdrawn after June 25, 2011. For a withdrawal to be effective, a written, telegraphic or facsimile transmission notice of withdrawal with respect to the Bronco shares must be timely received by the Depositary at one of its addresses set forth on the back cover of the Offer to Purchase, and the notice of withdrawal must specify the name of the person who tendered the Bronco shares to be withdrawn, the number of Bronco shares to be withdrawn and the name of the registered holder of Bronco shares, if different from that of the person who tendered such Bronco shares. If the Bronco shares to be withdrawn have been delivered to the Depositary, a signed notice of withdrawal with (except in the case of Bronco shares tendered by an Eligible Institution (as defined in the Offer to Purchase)) signatures guaranteed by an Eligible Institution must be submitted before the release of such Bronco shares. In addition, such notice must specify, in the case of Bronco shares tendered by delivery of certificates, the serial numbers shown on the specific certificates evidencing the Bronco shares to be withdrawn or, in the case of Bronco shares tendered by book-entry transfer, the name and number of the account at the Book-Entry Transfer Facility to be credited with the withdrawn Bronco shares. Withdrawals may not be rescinded, and Bronco shares withdrawn will thereafter be deemed not validly tendered. However, withdrawn Bronco shares may be retendered at any time before the expiration date by following the tender procedures described in Section 3 of the Offer to Purchase.

The exchange of Bronco shares for cash pursuant to the offer or the merger will be a taxable transaction for U.S. federal income tax purposes. All stockholders should consult with their own tax advisors as to the particular tax consequences of exchanging their Bronco shares pursuant to the offer or the merger.

The information required to be disclosed by paragraph (d)(1) of Rule 14d-6 of the General Rules and Regulations under the Securities Exchange Act of 1934, as amended, is contained in the Offer to Purchase and is incorporated herein by reference.

Bronco has provided to Purchaser its list of stockholders and security position listings for the purpose of disseminating the offer to holders of Bronco shares. The Offer to Purchase, the related Letter of Transmittal and other related materials will be mailed to record holders of Bronco shares and will be furnished to brokers, dealers, commercial banks, trust companies and similar persons whose names, or the names of whose nominees, appear on the stockholder list or, if applicable, who are listed as participants in a clearing agency’s security position listing, for subsequent transmittal to beneficial owners of Bronco shares.

The Offer to Purchase and the related Letter of Transmittal contain important information that should be read carefully before any decision is made with respect to the offer.

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Questions and requests for assistance and copies of the Offer to Purchase, the Letter of Transmittal and all other tender offer materials may be directed to the Information Agent at the address and telephone numbers set forth below and will be furnished promptly at Purchaser’s expense. Neither Chesapeake nor Purchaser will pay any fees or commissions to any broker or dealer or any other person (other than to the Information Agent for the offer and the Depositary) in connection with the solicitation of tenders of Bronco shares pursuant to the offer.

The Information Agent for the Offer is:

105 Madison Avenue

New York, NY 10016

(Call Collect) (212) 929-5500

or

Call Toll-Free (800) 322-2885

Email: tenderoffer@mackenziepartners.com

April 26, 2011

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