Exxon may try to upend its rival’s megadeal. The prize is a 30 percent stake in the oil-rich fields off the coast of Guyana.

Read More Oil (Petroleum) and Gasoline, Guyana, Exxon Mobil Corp, Chevron Corporation, Hess Corporation, Mergers, Acquisitions and Divestitures, Developing Countries, Natural Gas, Territorial Disputes, CNOOC Ltd, Venezuela, Stabroek block