Chevron is continuing to see "great gains" in its shale business, CEO Michael Wirth told CNBC on Tuesday.
In fact, the company just announced it has grown its position in the Permian Basin by 10 percent — from 2 million to 2.2 million acres.
"We're in early innings in terms of shale really performing," Wirth said in an interview with "Closing Bell."
While OPEC cut its production output last year, there has been a resurgence in U.S. production. According to the International Energy Agency, the U.S. will fulfill most of the world's growing demand for oil over the next five years.
However, former EOG Resources CEO Mark Papa, a pioneer in the industry, recently told The Wall Street Journal that he doesn't think U.S. production will keep growing as fast as the market thinks.
On Tuesday, U.S. crude futures rose 3 cents to settle at $62.60 a barrel. Brent crude futures rose 25 cents to settle at $65.79 a barrel.
Wirth, who took the helm of Chevron on Feb. 1, said the company's break-even price this year is $50 a barrel or better, without any asset sales.
The company also expects to generate about $14 billion in free cash flow this year, with about $8 billion going to the dividend. That leaves the company about $6 billion in excess cash flow, he said.
"We have a strong track record in both" dividends and cash buybacks and "intend to keep that up," he said.
However, while there is talk about reinstituting share buybacks, it is the fourth priority right now after the dividend, maintaining the business and reinvesting in the business.