Chevron CEO’s Career-Defining Win Means Healing Rift With Exxon

As the dust settles from a bruising legal battle over the world’s marquee oil bonanza, the leaders of Exxon Mobil Corp. and Chevron Corp. face a new challenge: collaboration.

Chevron’s victory in an international arbitration dispute initiated by Exxon allowed the $53 billion takeover of Hess Corp. to proceed. The prize for Chevron Chief Executive Officer Mike Wirth is a highly coveted stake in a cache of premiere oil discoveries in Guyana.

The catch is that Exxonis the majority owner and operator of those oil fields, which means two of the world’s largest energy behemoths must mend any lingering ...