Chevron's CEO is stepping down (CVX)

Reuters/Carlo Allegri

Chevron Corp Chief Executive John Watson is stepping down from his post atop the nation's second-largest oil company, according to a report from the Wall Street Journal.

A successor for Watson, 60, who has been the company's chairman and chief executive since 2010, has not been formally approved by the company's board. A leading candidate is Michael Wirth, 56, Chevron's vice chairman, the WSJ said.

Chevron spokespeople were unavailable to comment immediately. 

Chevron's directors believe Wirth would manage costs well in the new lower-oil-price environment that has changed the energy sector. 

Chevron's stock has gained 38% since Watson was appointed CEO.

NOW WATCH: THE BOTTOM LINE: New record highs for stocks and a deep dive into Apple's iPhone