ADVISORY AGREEMENT

Exhibit 10.1

ADVISORY AGREEMENT

This ADVISORY AGREEMENT (this “Agreement”) is entered into as of April 1, 2012 (the “Effective Date”), by and between Contango Oil & Gas Company, a Delaware corporation (“Contango”) and Juneau Exploration, L.P., a Texas limited partnership (“JEX”). Contango and JEX may be referred to herein collectively as the “Parties” or individually as a “Party”.

RECITALS

A. Contango is an independent oil and gas company whose core business is to explore, develop, produce and acquire natural gas and oil properties onshore and offshore in the Gulf of Mexico.

B. JEX is in the business of providing business, commercial and technical expertise with respect to oil and gas exploration prospects, oil and gas operations and the energy business.

C. JEX currently has six employees that JEX anticipates will provide advisory services to Contango.

D. Contango and JEX desire to enter into this Agreement to set forth the terms and conditions for JEX to provide advisory services to Contango in all phases of Contango’s business operations.

E. Contango has historically paid to JEX, in addition to other consideration, a $250,000 “prospect fee” for each oil and gas prospect generated by JEX and payments made hereunder shall substitute for such “prospect fee”.

NOW, THEREFORE, in consideration of the mutual covenants and agreements set forth herein, Contango and JEX agree, as follows:

1. Advisory Services.

a. Subject to the terms and conditions set forth in this Agreement, JEX shall perform in good faith such services as may be requested from time to time by the Chairman of Contango, including, but not limited to, the services (the “Services”) set forth in the Scope of Work attached hereto and incorporated herein as Exhibit A (“Scope of Work”). JEX agrees to perform the Services on an exclusive basis for Contango.

b. Contango may, from time to time, request changes in the Scope of Work. Any changes to the Scope of Work must be mutually agreed upon between JEX and Contango before they are incorporated in written amendments to Exhibit A of this Agreement.

c. JEX shall commence the Services on the Effective Date and shall perform all Services as required during the term of this Agreement.

2. Term of Agreement. This Agreement shall commence on the Effective Date and shall remain in full force and effect for a term of two (2) years and each month thereafter unless terminated upon ninety (90) days’ prior written notice by either Party (the “Term”).

3. Compensation. During the term of this Agreement and in consideration of the Services performed by JEX hereunder, JEX shall be entitled to receive the following compensation (“Compensation”):

a. Monthly fee of Sixteen Thousand Six Hundred and Sixty-Six Dollars ($166,666) per month, which amount shall be pro-rated for partial months.

b. Success Fees as defined in Exhibit B attached hereto.

c. Overriding Royalty Interests, Carried Interests in oil and gas production and Back-Ins in oil and gas prospects as described in Exhibit B attached hereto and separately agreed from time to time in agreements supplementing this Agreement.

d. Reimbursement for geological and geophysical expenses, legal costs, and other third party fees incurred by JEX as well as all other reasonable and necessary expenses incurred by JEX in providing the Services (collectively, “Reimbursable Expenses”).

4. Timing of Payments.

a. All Success Fees, Overriding Royalty Interests and Carried Interests shall be payable as set forth on Exhibit B attached hereto or separate agreements supplementing this Agreement.

b. Contango shall not withhold, nor shall Contango be obligated to withhold any, taxes or deductions from payments made to JEX. JEX shall pay, and shall be solely responsible for payment of any applicable taxes on payments made by Contango to JEX for Services rendered under this Agreement.

5. Ownership of Work Product. All reports, documents or other written material developed by JEX in the performance of this Agreement shall be and remain the property of Contango without restriction, claim, lien or limitation upon its use or dissemination by Contango.

6. Confidential Status; Disclosure of Information. All agreements, data, reports, documents, materials or other information developed or received by JEX or provided to JEX by or on behalf of Contango shall be deemed confidential and shall not be disclosed by JEX without the prior written consent of Contango. Contango shall grant such consent if disclosure is legally required by applicable law.

7. Independent Contractor.

a. JEX is an independent contractor and shall have no power to bind Contango or to incur any debt, obligation or liability on behalf of Contango. Contango shall not have power to bind JEX or to incur any debt, obligation or liability on behalf of JEX.

b. JEX shall pay all required taxes on amounts paid to JEX under this Agreement.

c. JEX shall fully comply with all applicable laws in rendering the Services.

2

d. Contango is not and shall not be obligated to provide any employee benefits to JEX.

8. Indemnification. To the fullest extent permitted by law, each of JEX and Contango shall, at its sole respective cost and expense, defend, protect, indemnify, and hold harmless the other Party and, as applicable, its respective officers, attorneys, agents, employees, successors, and assigns (collectively, “Indemnitees”) from and against any and all damages, costs, expenses, liabilities, claims, demands, causes of action, proceedings, expenses, judgments, penalties, liens, and losses of any nature whatsoever, including fees of accountants, attorneys, expert witnesses, or other professionals and all costs associated therewith (collectively, “Claims”), resulting from any negligent act, error, omission or failure to act by the indemnifying Party (“Indemnitor”) or, as applicable, its respective officers, agents, servants, employees, subcontractors, material men, suppliers or their respective officers, agents, servants or employees in connection with, resulting from, or related to this Agreement or for failure to perform or negligent performance of any term, provision, covenant, or condition of the Agreement, including this indemnity provision. This indemnity provision is effective regardless of any prior, concurrent, or subsequent passive negligence by Indemnitees and shall operate to fully indemnify Indemnitees against any such negligence. This indemnity provision shall survive the termination of the Agreement and is in addition to any other rights or remedies which Indemnitees may have under the law or at equity. Payment is not required as a condition precedent to an Indemnitee’s right to recover under this indemnity provision, and an entry of judgment against Indemnitor shall be conclusive in favor of the Indemnitee’s right to recover under this indemnity provision. Indemnitor shall pay Indemnitees for any attorneys’ fees and costs incurred in enforcing this indemnification provision. This indemnity is effective without reference to the existence or applicability of any insurance coverages which may have been required under this Agreement or any additional insured endorsements which may extend to Indemnitees. This indemnity provision shall survive the termination of this Agreement and is in addition to any other rights or remedies which Indemnitees may have under the law.

9. Limitations on Liability. Notwithstanding anything to the contrary, neither Party shall be liable to the other Party for any punitive, incidental, special, exemplary or consequential damages arising in connection with or with respect to this Agreement.

10. Limits of JEX Responsibility. JEX assumes no responsibility other than to render the Services described herein in good faith and shall not be responsible for any action of Contango in following or declining to follow any advice or recommendation of JEX. JEX, its partners, officers, employees and affiliates will not be liable to Contango, its shareholders, or others, except by reason of acts constituting bad faith, willful or wanton misconduct or gross negligence. Contango recognizes that Mr. John B. Juneau in his capacity as a Director of Contango pursuant to Section 17 and in his capacity as an executive for JEX may from time to time result in a conflict of interest and Contango hereby waives any prospective conflict of interest that may result from the dual positions. Contango shall reimburse, indemnify and hold harmless JEX, its partners, officers and employees and its affiliates for and from any and all expenses (including reasonable attorneys’ fees), losses, damages, liabilities, demands, charges and claims of any nature whatsoever in respect to or arising in connection with any acts or omissions of JEX and its affiliates and any acts or omissions of JEX undertaken in good faith and in accordance with the standard set forth above.

3

11. Mutual Cooperation.

a. Contango shall provide JEX with all pertinent data, documents and other requested information as is reasonably available for the proper performance of the Services by JEX.

b. In the event any claim or action is brought by a third party against Contango relating to JEX’s performance in connection with this Agreement, JEX shall render any assistance that Contango may reasonably request.

12. Notices.

Any notices, bills, invoices, or reports required by this Agreement shall be deemed received on: (a) the day of delivery if delivered by hand or overnight courier service during Contango’s and JEX’s regular business hours; or (b) on the third (3rd) business day following deposit in the United States mail, postage prepaid, to the addresses heretofore below, or to such other addresses as the Parties may, from time to time, designate in writing.

If to Contango:

Contango Oil & Gas Company

3700 Buffalo Speedway, Suite 960

Houston, Texas 77098

Attention: Kenneth R. Peak

Phone: (713)  ###-###-####

Fax: (713)  ###-###-####

If to JEX:

Juneau Exploration L.P.

3700 Buffalo Speedway, Suite 925

Houston, Texas 77098

Attention: John B. Juneau

Phone: (713)  ###-###-####

Fax: (713)  ###-###-####

13. Governing Law. This Agreement shall be interpreted, construed and enforced in accordance with the laws of the State of Texas.

14. Dispute Resolution; Arbitration. In the event that there is any controversy, claim or dispute between the Parties arising out of or related to this Agreement, the Parties shall for a period of thirty (30) attempt in good faith to negotiate a resolution. If the Parties are unable in such time period to resolve the controversy, claim or dispute, either Party may, by written notice to the other Party, request that the matter be submitted to arbitration under and pursuant to the applicable commercial arbitration rules and procedures of the American Arbitration Association. The arbitration shall be held in Houston, Texas. The arbitrator(s) shall have no affiliation or relationship with either Party or their counsel and, when feasible, shall have training or

4

experience in the subject matter of the dispute. Any award or decision rendered pursuant to such rules and procedures shall be final and binding on each of the Parties hereto and their respective successors and assigns. Such decision or award shall be in writing signed by the arbitrator(s) and shall state the reasons upon which the decision or award is based. The arbitrator(s), in deciding any dispute, controversy or claim arising under this Agreement as provided in this Section 14, shall look to the substantive laws of the State of Texas for the resolution of the dispute, controversy or claim. Judgment on any decision or award pursuant hereto may be entered in any court having jurisdiction thereof.

15. No Partnership or Joint Venture. Contango and JEX are not partners or joint venturers with each other and neither the terms of this Advisory Agreement nor the fact that Contango and JEX have joint interests in any one or more investments shall be construed so as to make them partners or joint venturers or impose any liability as such partners or joint venturers or impose any liability as such on either of them.

16. Fidelity Bond. JEX shall not be required to obtain or maintain a fidelity bond in connection with the performance of its services hereunder.

17. Board of Directors. During the Term, Contango agrees to nominate Mr. John B. Juneau as a member of the Board of Directors of Contango and use its reasonable commercial efforts to cause Mr. John B. Juneau to be elected to the Board of Directors. Mr. John B. Juneau shall be compensated in the same or similar manner as all other independent Directors of Contango and shall be subject to the same or similar rights and obligations of all other independent Directors, including inclusion in all insurance coverages that Contango may have for its officers and directors while serving in the capacity as a Director of Contango.

18. Contaro Company Termination. Contango, as the sole shareholder of Contaro Company, and JEX hereby terminate the Advisory Agreement dated as of the date hereof.

19. JEX Interests. Nothing herein shall prevent JEX from (i) continuing to own a membership interest in Republic Exploration, LLC, which may enter into agreements from time to time with Contango and its affiliates, and (ii) enter into agreements from time to time with Contango and its affiliates for oil and gas exploration prospects where JEX, or its employees, may receive overriding royalty interests and/or carried interests.

20. Further Assurances. Each of the Parties hereto shall do such further acts, shall perform such further actions, and shall execute and deliver such additional agreements and instruments as the other Party may reasonably require to consummate, evidence or confirm the agreements and understandings contained herein in the manner contemplated hereby.

21. No Assignment. JEX shall not assign or transfer any interest in this Agreement nor the performance of any of JEX’s obligations hereunder, nor shall it subcontract any of the Services or the Scope of Work without the prior written consent of Contango.

5

22. Time Is Of The Essence. Time is hereby expressly declared to be of the essence of this Agreement and of each and every provision hereof; and each and every provision hereof is hereby declared to be and made a material, essential and necessary part of this Agreement.

23. Exhibits; Precedence. All documents referenced as exhibits in this Agreement are hereby incorporated in this Agreement. In the event of any material discrepancy between the express provisions of this Agreement and the provisions of any document incorporated herein by reference, the provisions of this Agreement shall prevail.

24. Entire Agreement and Amendments. This Agreement, and any other documents incorporated herein by specific reference, represent the entire and integrated agreement between JEX and Contango. This Agreement supercedes all prior oral or written negotiations, representations or agreements. This Agreement may not be amended, nor any provision or breach hereof waived, except in a writing signed by the Parties which expressly refers to this Agreement.

25. Severability. Wherever possible, each provision of this Agreement shall be interpreted in such a manner as to be valid under applicable law. If any provision of this Agreement, is determined by a court of competent jurisdiction to be invalid, void or unenforceable, the remaining provisions shall nevertheless continue in full force and effect.

26. Counterparts. This Agreement may be executed in any number of counterparts, each of which shall be deemed an original, but all of which when taken together shall constitute one and the same instrument.

[Remainder of Page Intentionally Left Blank]

6

WHEREFORE, the Parties hereto have executed this Agreement as of the date first above written.

Exhibit A

Scope of Work

(1) JEX will direct the operations of Contango and will provide advisory services to all phases of the business of Contango, including oil and gas exploration prospects, oil and gas operations and new energy ventures.

(2) John B. Juneau will serve on the Board of Directors of Contango and the board of managers or board of directors of each subsidiary of Contango as may be necessary or desirable, including the board of managers of Exaro Energy III, LLC so long as Contaro Company holds a membership interest in Exaro Energy III, LLC.

Exhibit B

Success Fees

JEX shall be entitled to receive a fee equal to one percent (1%) of the cash profit earned by Contaro Company. Cash Profit is defined as the amount of cash received by Contango as a result of its investment in Contaro Company, less the cash invested by Contango as a result of its investment in Contaro Company.

Overriding Royalty Interests

JEX may receive, or the employees of JEX may receive, an overriding royalty interest in oil and gas exploration prospects generated by JEX as Contango and JEX may agree from time to time.

Carried Interests

JEX may receive, or employees of JEX may receive, a carried interest in oil and gas exploration prospects generated by JEX as Contango and JEX may agree from time to time.

Back-Ins

JEX may receive, or employees of JEX may receive, at a certain point in the development process, an election to increase its interest in oil and gas exploration prospects by an additional working interest, free and clear of all costs and expenses attributable prior to such election.