Eric Reynolds will tell you that he is on the verge of freeing much of humanity from the deadly scourge of the cooking fire. He can halt the toxic smoke wafting through African homes, protect what is left of the continent’s forest cover and help rescue the planet from the wrath of climate change.

He is happy to explain, at considerable length, how he will systematically achieve all this while constructing a business that can amass billions in profit from an unlikely group of customers: the poorest people on earth.

He will confess that some people doubt his hold on reality.

“A lot of people think it’s too good to be true,” says Mr. Reynolds, a California-born entrepreneur living in Rwanda. “Most people think I am pretty out there.”

The company he is building across Rwanda, Inyenyeri, aims to replace Africa’s overwhelming dependence on charcoal and firewood with clean-burning stoves powered by wood pellets. The business has just a tad more than 5,000 customers and needs perhaps 100,000 to break even. Even its chief operating officer, Claude Mansell, a veteran of the global consulting company Capgemini, wonders how the story will end.

“Do we know that it’s going to work?” he asks. “I don’t know. It’s never been done before.”

Inyenyeri presents a real-world test of an idea gaining traction among those focused on economic development — that profit-making businesses may be best positioned to deliver critically needed services to the world’s poorest communities.

Governments in impoverished countries lack the finance to attack threats to public health, and many are riddled with corruption (though, by reputation, not Rwanda’s). Philanthropists and international aid organizations play key roles in areas such as immunizing children. But turning plans for basic services into mass-market realities may require the potent incentives of capitalism. It is a notion that has provoked the creation of many businesses, most of them failures.

“Profit feeds impact at scale,” says Mr. Reynolds, now in the midst of a global tour as he courts investment on top of the roughly $12 million he has already raised. “Unless somebody gets rich, it can’t grow.”

More than four decades have passed since Mr. Reynolds embarked on what he portrays as an accidental life as an entrepreneur, an outgrowth of his fascination with mountaineering. He dropped out of college to start Marmot, the outdoor gear company named for the burrowing rodent. There, he profited by protecting Volvo-driving, chardonnay-sipping weekend warriors against the menacing elements of Aspen. Now, he is trying to build a business centered on customers for whom turning on a light switch is a radical act of upward mobility.

Inyenyeri is betting that it can give away stoves and make money by charging people for fuel. If it succeeds, it vows to deliver virtues that go well beyond the bottom line.

The forests would be spared, because making wood pellets requires far fewer trees than wood fires and charcoal. Customers would gain a reprieve from ailments related to smoke from cooking, including cataracts, heart disease and respiratory ailments that, in many countries, kill more people than malaria, H.I.V. and tuberculosis combined.

Rwandans in rural areas — and, eventually, across Africa and South Asia — would be freed from the time-sucking drudgery of having to look for wood. People in cities, who rely on charcoal, could switch to cheaper wood pellets, using the savings to buy health care, food and school uniforms.

In much of the developing world, initiatives aimed at sparing the environment tend to pit the livelihoods of poor people against the protection of natural resources. Peasants in the Amazon are supposed to stop hacking away at forests to clear land for crops so the rest of the planet can benefit from a reduction in carbon emissions. Yet in Inyenyeri’s designs, the everyday concerns of poor households are aligned with environmental imperatives, because people prefer to cook with the stoves.

At 66, with sunburned cheeks and intense blue eyes, Mr. Reynolds can at times sound like the latest white man come to save Africa. “It’s just outrageous that we have three billion people still cooking in the Stone Age,” he says. “It’s entirely solvable.”

He touts his ability to connect with customers, the women who do the cooking in Rwanda, though even after a decade living in the country he does not speak the local language, Kinyarwanda. He sits on the dirt floors of villagers’ homes and speaks English slowly and loudly, exaggerating each syllable. Rwandan women trust him, he says, because he married one. He hands them his phone and displays the proof — pictures of his wife, Mariam Uwizeyimana Reynolds, 32, and their two fresh-faced boys, Terry Toulumne Reynolds, 6, and Marc Booth Reynolds, 3.