BRNC Bronco Drilling Company, Inc. (MM)

UNITED STATES SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE TO

Tender Offer Statement under Section 14(d)(1) or 13(e)(1)

of the Securities Exchange Act of 1934

(Amendment No. 3)

BRONCO DRILLING COMPANY, INC.

(Name of Subject Company)

NOMAC ACQUISITION, INC.

CHESAPEAKE ENERGY CORPORATION

(Names of Filing Persons — Offeror)

Common Stock, Par Value $0.01 Per Share

(Title of Class of Securities)

112211107

(Cusip Number of Class of Securities)

Jennifer M. Grigsby

Senior Vice President, Treasurer and

Corporate Secretary

6100 North Western Avenue

Oklahoma City, Oklahoma 73118

Telephone: (405) 848-8000

(Name, Address and Telephone Number of Person Authorized to Receive Notices

and Communications on Behalf of Filing Persons)

Copies to :

CALCULATION OF FILING FEE

Check the appropriate boxes below to designate any transactions to which the statement relates:

Check the following box if the filing is a final amendment reporting the results of the tender offer.   ¨

This Amendment No. 3 (this “ Amendment No. 3 ”) amends and supplements the Tender Offer Statement on Schedule TO (together with any amendments and supplements thereto, the “ Schedule TO ”) filed with the Securities and Exchange Commission (the “ SEC ”) on April 26, 2011, as amended by the Amendment No. 1 to the Schedule TO filed on May 3, 2011 and by the Amendment No. 2 to the Schedule TO filed on May 5, 2011, and is filed by (i) Nomac Acquisition, Inc., a Delaware corporation (“ Purchaser ”) and an indirect wholly owned subsidiary of Chesapeake Energy Corporation, an Oklahoma corporation (“ Chesapeake ”), and (ii) Chesapeake. The Schedule TO relates to the tender offer by Purchaser and Chesapeake 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 ”), at $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, copies of which were filed with the Schedule TO as Exhibits (a)(1)(A) and (a)(1)(B), respectively (which, together with any amendments or supplements, collectively constitute the “ offer ”). The offer is made pursuant to the Agreement and Plan of Merger, dated as of April 14, 2011 and amended as of May 17, 2011 (the “ merger agreement ”), by and among Chesapeake, Purchaser and Bronco.

The information in the Offer to Purchase and the related Letter of Transmittal is incorporated in this Amendment No. 3 by reference to all of the applicable items in the Schedule TO, except that such information is amended and supplemented to the extent specifically provided in this Amendment No. 3. Capitalized terms used and not otherwise defined in this Amendment No. 3 shall have the meanings assigned to such terms in the Offer to Purchase or in the Schedule TO.

Items 1 through 11. Summary Term Sheet; Subject Company Information; Identity and Background of Filing Person; Terms of the Transaction; Past Contacts, Transactions, Negotiations and Agreements; Purposes of the Transaction and Plans or Proposals; Source and Amount of Funds or Other Consideration; Interest in Securities of the Subject Company; Persons/Assets Retained, Employed, Compensated or Used; Financial Statements; Additional Information.

Ten putative class action lawsuits relating to the merger agreement and the transactions contemplated therein have been commenced against Bronco and current members of the Bronco Board, including Bronco’s chief executive officer (the “ Individual Defendants ”). Six putative class action lawsuits were filed in the District Court of Oklahoma County, Oklahoma (collectively, the “ Oklahoma Suits ”). All but one of the Oklahoma Suits have been voluntarily dismissed. Four putative class action lawsuits were filed in the Court of Chancery of the State of Delaware (the “ Delaware Suits ” and together with the one remaining Oklahoma Suit, the “ Class Actions ”). The Class Actions each seek certification of a class of all holders of Bronco’s common stock and variously allege, among other things, that: (1) the Individual Defendants have breached and continue to breach their fiduciary duties to the stockholders of Bronco; (2) the offer and the merger are unfair to the public stockholders of Bronco as the proposed transactions underestimate the value of Bronco; (3) the Individual Defendants are pursuing a course of conduct that does not maximize the value of Bronco; and (4) Bronco aided and abetted the alleged breaches of duties by the Individual Defendants. The Delaware Suits also name Chesapeake and Purchaser as defendants, in each case alleging that Chesapeake and Purchaser aided and abetted the alleged breaches of duties by the Individual Defendants. On April 29, 2011, one of the Delaware Suits was amended, adding allegations that Bronco’s 14D-9 and Chesapeake’s Schedule TO did not adequately describe the process that resulted in the offer and that Bronco’s 14D-9 did not include adequate information concerning the fairness opinion Johnson Rice & Company L.L.C. provided to the Bronco Board. The Delaware Suits were consolidated into a single action on May 6, 2011. On May 10, 2011, the Oklahoma Suit was stayed in favor of the Delaware Suits. The Class Actions seek, among other things, an injunction prohibiting consummation of the tender offer and the merger, attorneys’ fees and expenses and rescission or damages in the event the proposed transactions are consummated. A preliminary injunction hearing has been scheduled in the Delaware Suits for May 19, 2011. We believe the Class Actions are entirely without merit.

2

On May 17, 2011, the parties to the Delaware Suits informed the Court of Chancery that they had reached an agreement in principle, which, if approved by the Court, would result in the settlement of all claims brought on behalf of the purported class. Pursuant to that agreement: (i) Chesapeake, Bronco and Purchaser have agreed to amend the merger agreement to shorten from twelve (12) months to nine (9) months the period during which, if Bronco enters into a definitive Contract to consummate, or consummates any transaction contemplated by any Takeover Proposal, Bronco must pay Chesapeake the Termination Fee (as those terms are defined in the merger agreement); (ii) Bronco will make additional disclosures in an amendment to its Schedule 14D-9; and (iii) Chesapeake and Purchaser will extend the expiration of the offer from 12:00 midnight New York City time at the end of Monday, May 23, 2011 to 12:00 midnight New York City time at the end of Tuesday, May 31, 2011. The parties have entered into a memorandum of understanding memorializing the key terms of that agreement. The memorandum of understanding is attached as Exhibit a(5)(Q) hereto and is incorporated by reference.

The Individual Defendants, Bronco, Chesapeake and Purchaser have denied, and continue to deny, that they have committed or aided and abetted in the commission of any violation of law or engaged in any of the alleged wrongful acts, and expressly maintain that they diligently and scrupulously complied with their fiduciary and other legal duties.

(a) the second paragraph in Section 11 – “ Background of the Offer ” on page 17 of the Offer to Purchase in the section entitled “The Offer” is hereby amended and restated as follows:

On October 27, 2010, a representative of Jefferies & Company, Inc. (“ Jefferies ”) contacted Zachary M. Graves, Bronco’s Executive Vice President of Operations. Among other topics, the Jefferies representative suggested that Chesapeake was interested in growing its service assets as part of its ongoing vertical integration strategy and to meet drilling commitments and growth targets. In the event that Chesapeake was interested in acquiring Bronco, Mr. Graves and the representative of Jefferies discussed that because of Chesapeake’s vertical integration strategy, it might result in a superior offer than could be obtained from another service company or financial buyer. At the time, Jefferies was not engaged on behalf of Bronco or Chesapeake.

(b) the third paragraph in Section 11 – “ Background of the Offer ” on page 17 of the Offer to Purchase in the section entitled “The Offer” is hereby amended and restated as follows:

On October 29, 2010, a representative of Jefferies called Mr. Graves to confirm that Chesapeake was interested in discussing a potential acquisition of Bronco. At the time, Jefferies was not engaged on behalf of Bronco or Chesapeake.

(c) the seventh paragraph in Section 11 – “ Background of the Offer ” on page 17 of the Offer to Purchase in the section entitled “The Offer” is hereby amended and restated as follows:

On November 10, 2010, Aubrey K. McClendon, Chesapeake’s Chairman of the Board of Directors and Chief Executive Officer, Domenic J. Dell’Osso, Jr., Chesapeake’s Chief Financial Officer, and other representatives of Chesapeake’s management met with Messrs. Harrison, Graves, Dubberstein and Porter of Bronco, together with Jefferies, at which meeting they discussed Bronco’s business, rig fleet and initiatives to reduce its indebtedness, including Bronco’s ongoing strategic divestiture of some of its drilling rigs that were not suited to horizontal drilling in domestic shale plays. At the meeting, discussions ensued regarding additional financial and operational information concerning Bronco’s drilling rigs that Chesapeake would require before it could establish a value for Bronco.

(d) the eighteenth paragraph in Section 11 – “ Background of the Offer ” on page 18 of the Offer to Purchase in the section entitled “The Offer” is hereby amended and restated as follows:

From March 31, 2011 through April 11, 2011, Jefferies requested from Johnson Rice certain additional financial and operating data for Bronco, including, among other things, drilling rig status reports, drilling rig contract data, the February 2011 balance sheet and information relating to Bronco’s joint ventures in Mexico and Libya, which data was supplied by Johnson Rice and Bronco’s management.

(e) the first sentence of the nineteenth paragraph in Section 11 – “ Background of the Offer ” on page 18 of the Offer to Purchase in the section entitled “The Offer” is hereby amended and restated as follows:

On April 4, 2011, Mr. McClendon sent a letter to Mr. Harrison indicating that Chesapeake remained interested in a potential acquisition of Bronco and that, based upon the increase in Bronco’s share price since Chesapeake’s initial proposal, it had revisited its valuation metrics and was prepared to offer $11.00 per share in cash, representing an approximately 2.8% discount to the previous day’s close of $11.32 per share, a 14% premium to the thirty day average market price of Bronco shares and a 45% premium to the ninety day average price.

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The letter indicated that the proposal was subject only to the completion of customary due diligence and the negotiation and execution of mutually acceptable definitive documentation.

If:

then Bronco will pay Chesapeake a termination fee equal to $13,000,000, plus expenses (without duplication if paid under any other provision of the merger agreement) of up to $1,500,000.

On May 18, 2011, Chesapeake and Purchaser announced that the expiration of the Offer was extended until 12:00 Midnight, New York City time, at the end of Tuesday, May 31, 2011. Accordingly, the term “Expiration Date” means 12:00 Midnight, New York City time, at the end of Tuesday, May 31, 2011, unless further extended, in which event “expiration date” means the latest time and date at which the offer, as so extended, will expire. A copy of the press release announcing the extension of the Offer is attached hereto as Exhibit (a)(5)(P) and is incorporated by reference.

All references to the Agreement and Plan of Merger, dated as of April 14, 2011, by and among Chesapeake Energy Corporation, Nomac Acquisition, Inc. and Bronco Drilling Company, Inc. are hereby deemed to be references to the Agreement and Plan of Merger, dated as of April 14, 2011 and amended as of May 17, 2011, by and among Chesapeake Energy Corporation, Nomac Acquisition, Inc. and Bronco Drilling Company, Inc.

Item 12 of the Schedule TO is hereby amended and supplemented by adding the following exhibits:

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SIGNATURES

After due inquiry and to the best knowledge and belief of the undersigned, each of the undersigned certify that the information set forth in this statement is true, complete and correct.

Dated: May 18, 2011

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