UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of the

Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): May 23, 2011 (May 17, 2011)

BRONCO DRILLING COMPANY, INC.

(Exact name of Registrant as specified in its charter)

Registrant’s telephone number, including area code: (405) 242-4444

(Former name, former address and former fiscal year, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

Amendment to Merger Agreement

As previously reported, on April 14, 2011, Bronco Drilling Company, Inc., a Delaware corporation (the “Company”), entered into an Agreement and Plan of Merger (as amended on May 17, 2011, the “Merger Agreement”) with Chesapeake Energy Corporation, an Oklahoma corporation (“Chesapeake”), and Nomac Acquisition, Inc., a Delaware corporation and an indirect wholly owned subsidiary of Chesapeake (“Merger Sub”). Pursuant to the Merger Agreement and upon the terms and subject to the conditions thereof, on April 26, 2011, Merger Sub commenced a tender offer (the “Offer”) to purchase all of the issued and outstanding shares of the common stock of the Company, par value $0.01 per share (the “Shares”), for $11.00 per share in cash, without interest and less any required withholding taxes (such amount, the “Offer Price”).

On May 17, 2011, in connection with the memorandum of understanding described below, the Company, Chesapeake and Merger Sub entered into an amendment to the Merger Agreement (the “Amendment”) pursuant to which (i) the Company consented to Merger Sub’s extension of the expiration date of the Offer from May 23, 2011 to May 31, 2011 and (ii) the period following a termination of the Merger Agreement when the Termination Fee (as defined in the Merger Agreement) may be payable under the limited circumstances specified in the Merger Agreement was reduced from twelve (12) months to nine (9) months.

The Merger Agreement, as amended, remains in full force and effect. The foregoing description of the Merger Agreement is qualified by reference to the full text of the Merger Agreement, which is included as Exhibit 2.1 to the Company’s Current Report on Form 8-K filed by the Company as of April 18, 2011 and is incorporated by reference to this Item 1.01. The foregoing description of the Amendment is qualified by reference to the full text of the Amendment, which is included as Exhibit (d)(4) to Amendment No. 3 to the Tender Offer Statement on Schedule TO filed by Chesapeake and Merger Sub as of May 18, 2011 and is incorporated by reference to this Item 1.01.

Ten putative class action lawsuits relating to the Merger Agreement and the transactions contemplated therein were commenced against the Company. Six of these suits were filed in the District Court of Oklahoma County, Oklahoma (collectively, the “Oklahoma Suits”), and four were filed in the Court of Chancery of the State of Delaware (the “Delaware Suits”). All but one of the Oklahoma Suits have been voluntarily dismissed. On May 6, 2011, the Delaware Suits were consolidated into a single action. On May 10, 2011, the remaining Oklahoma Suit was stayed in favor of the Delaware Suits. These suits name as defendants the Company, the members of the Company’s board of directors, and in certain instances, Chesapeake and Merger Sub.

While the Company and the other defendants believe that each of the aforementioned lawsuits is without merit and that they have valid defenses to all claims, in an effort to minimize the cost and expense of any litigation relating to such lawsuits, on May 17, 2011, the Company and other defendants entered into a memorandum of understanding (the “MOU”) with the parties to the Delaware Suits pursuant to which the Company and such parties agreed in principle, and subject to certain conditions, to settle those lawsuits. Subject to approval of the Delaware Court of Chancery and further definitive documentation, the MOU establishes a framework to resolve the Delaware Suits against the Company and the other defendants in connection with the Merger Agreement and contemplates a release and settlement of all claims against the Company and other defendants and their affiliates and agents in connection with the Merger Agreement. In exchange for such release and settlement, pursuant to the terms of the MOU, the parties agreed that (i) the Company, Chesapeake, and Merger Sub would modify the Merger Agreement to reflect the Amendment described above, (ii) the Company would provide additional disclosures in an amendment to its Solicitation/Recommendation Statement on Schedule 14D-9, which amendment was filed on May 18, 2011 and (iii) Chesapeake and Merger Sub would 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 settlement is also contingent upon, among other things, consummation of the Merger (as defined in the Merger Agreement).

On May 20, 2011, the Delaware Court of Chancery granted a motion filed by the plaintiffs in the Delaware

Suits to certify a class. The order entered by the Court, among other things, certified a class consisting of all record and beneficial holders of the Company’s common stock at any time between April 14, 2011 and the date of consummation of the merger (the “Class”). Excluded from the Class are the Company, Chesapeake, Merger Sub, D. Frank Harrison, Richard B. Hefner, Gary C. Hill, David W. House and William R. Snipes or any of their respective families, parent entities, controlling persons, associates, predecessors, successors, affiliates or subsidiaries, and each and all of their respective past or present officers, directors, stockholders, principals, representatives, employees, attorneys, financial or investment advisors, consultants, accountants, investment bankers, commercial bankers, entities providing fairness opinions, underwriters, brokers, dealers, advisors or agents, heirs, executors, trustees, general or limited partners or partnerships, limited liability companies, members, managers, joint ventures, personal or legal representatives, estates, administrators, predecessors, successors and assigns. In addition, the Court certified plaintiffs to the Delaware Suits as the representatives of the Class and their counsel as co-lead counsel for the Class.

In the event the settlement anticipated by the MOU is not approved, the Company will continue to vigorously defend these actions. This summary of the MOU does not purport to be complete and is qualified in its entirety by reference to the MOU, which is included as Exhibit (a)(5)(O) to the Company’s Amendment No. 2 to the Solicitation/Recommendation Statement on Schedule 14D-9 filed by the Company as of May 18, 2011 and is incorporated by reference to this Item 8.01.

On May 18, 2011, Chesapeake and the Company issued a joint press release announcing the entry into the Amendment and the MOU. The press release is included as Exhibit (a)(5)(P) to Amendment No. 3 to the Tender Offer Statement on Schedule TO filed by Chesapeake and Merger Sub as of May 18, 2011 and is incorporated by reference to this Item 8.01.

Notice to Investors

This Current Report on Form 8-K is neither an offer to purchase nor a solicitation of an offer to sell any securities. The Offer described in this report commenced on April 26, 2011, and, in connection with the Offer, Chesapeake has caused Merger Sub to file with the SEC a tender offer statement on Schedule TO (including the offer to purchase, letter of transmittal and related tender offer documents). The Company has filed with the SEC a solicitation/recommendation statement with respect to the tender offer on Schedule 14D-9. Investors and the Company’s stockholders are advised to read carefully these documents, and the amendments thereto that have been or will be filed with the SEC, because they contain important information. These documents are available to all stockholders of the Company at no expense to them. These documents are also available at no charge from the SEC’s website at www.sec.gov. In addition, investors and stockholders of the Company may obtain a free copy of these documents from the Company by contacting Bronco Drilling Company, Inc. at 16217 N. May Ave., Edmond, OK 73013, attention: Investor Relations.

Forward Looking Statements

Certain statements either contained in or incorporated by reference into this document are “forward-looking statements.” These forward-looking statements generally include statements that are predictive in nature, depend upon or refer to future events or conditions, and are based on current expectations and assumptions that are subject to risks and uncertainties which may cause actual results to differ materially from the forward looking statements. Such forward-looking statements include the ability of the Company, Chesapeake and Merger Sub to complete the transactions contemplated by the Merger Agreement, including the parties’ ability to satisfy the conditions to the consummation of the Offer and the other conditions set forth in the Merger Agreement and the possibility of any termination of the Merger Agreement. Actual results may differ materially from current expectations because of risks associated with uncertainties as to the timing of the Offer and the subsequent Merger; uncertainties as to how many of the Company’s stockholders will tender their Shares in the Offer; the risk that competing offers or acquisition proposals will be made; the possibility that various conditions to the consummation of the Offer or the subsequent Merger may not be satisfied or waived; the effects of disruption from the transactions on the Company’s business and the fact that the announcement and pendency of the transactions may make it more difficult to establish or maintain relationships with employees, suppliers and other business partners; the risk that stockholder litigation in connection with the Offer or the Merger Agreement may result in significant costs of defense, indemnification and liability; the risk that the MOU may not be approved or its conditions may not be satisfied; other uncertainties pertaining to the business of the Company, including, among other things, the risks detailed in the Company’s public filings with the SEC from time to time, including the Company’s most recent Annual Report on Form 10-K for the

year ended December 31, 2010. The reader is cautioned not to unduly rely on these forward-looking statements. The Company expressly disclaims any intent or obligation to update or revise publicly these forward-looking statements except as required by law.

(d) Exhibits

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the Company has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.