San Ramon, Calif.

It's the day after President Obama delivered his most recent vision of America's energy future, and I'm sitting in the sunny corporate offices of Chevron, the country's second-largest oil company. Let's just say John Watson has a different view.

The Chevron CEO is a rare breed these days: an unapologetic oil man. For decades—going back to Jimmy Carter—politicians have been peddling an America free of fossil fuels. Mr. Obama has taken that to an unprecedented level, closing off more acreage to drilling, pouring money into green energy, pushing new oil company taxes, instituting anticarbon regulations. America is going backward on affordable energy, even as oil hits $110 a barrel.

Enter the tall, bespectacled Mr. Watson, who a little more than a year ago stepped into the shoes of longtime CEO David O'Reilly. An economist by training, soft-spoken by nature, the 53-year-old Mr. Watson is hardly some swaggering wildcatter. Yet in a year of speeches, he has emerged as one of the industry's foremost energy realists. No "Beyond Petroleum" (BP) for him. On energy, he says, America "has a lot to learn."

Starting with the argument—so popular among greens and Democrats—that we are running out of oil. "Peak oil"—the theory that global oil production will soon hit maximum levels and begin to decline—is a favorite among this crowd, and it is one basis for their call for more biofuels and solar power. Mr. Watson doesn't dismiss the idea but explains why it remains largely irrelevant.