Say what you will about Shai Agassi, but no one will accuse him of thinking small. Agassi, who recently turned 40, has never worked in the energy industry or the automobile business. But he trying to turn both industries upside down by getting the world to embrace electric cars. And he is making surprising progress.

Shai was the opening speaker at FORTUNE’s Brainstorm: Green conference last week, and I wish we’d given him more time to talk about his very big idea: What he wants to do is create a new kind of battery-powered car, equip metropolitan areas and eventually entire nations with charging stations, drive demand for renewable energy and, not incidentally, create a new model for selling cars and fuel.

“Project Better Place” – that’s the name of his company – “started out with a simple question: how do you run a country without oil?” Shai told me.

He wasn’t thinking about just any country; he was thinking about his home land of Israel, which wants to reduce the world’s dependence on oil, for obvious reasons. So, of course, should the United States, and not merely to reduce emissions of greenhouse gases. Oil-producing nations Saudi Arabia, Russia, Venezuela and Sudan are not exactly beacons of freedom and democracy.

As Agassi tells his story, he was on his way to becoming the CEO of software giant SAP when he left to start Project Better Place. Getting the new company off the ground was not easy. He pitched his idea to more than 200 investors before raising about $200 million. His biggest investor is Israel Corp., an Israeli holding and oil company, which invested $100 million. He also raised money from venture capital firm VantagePoint Venture Partners and Morgan Stanley, and from a handful of individual investors, including James Wolfensohn, the former president of the World Bank, and Seagram’s heir Edgar Bronfman.

He says that January 21, 2008 was “the day that changed the world.” That day, the company announced that the state of Israel would support his efforts to build a national infrastructure for electric cars, and that Carlos Ghosn, the chief executive of Nissan and Renault, had agreed to begin producing the vehicles on a commercial scale in 2010. Several months later, Shai went to Denmark to make a similar announcement—some, but not all, of the country would support his plan. He hopes to persuade several other European nations get behind Project Better Place by the end of the year. He also expects other carmakers to come along.

As Agassi puts it: “One train has left. Carlos Ghosn is in the lead. And we know where the train is going. It’s going to Jerusalem.”

How does the business work? Essentially, by exploiting what Agassi argues are the cost advantages of electric cars over vehicles powered by gasoline and, yes, you read that right—he says it’s significantly cheaper to operate an electric car than a gas-powered one, particularly with oil priced at more than $110 a barrel. (The economics work with much cheaper oil, too, he says.) The low-cost advantage for electric cars is even greater in Europe, he says, where gas prices are the equivalent of $7 to $9 a gallon.

His claim depends on a lot of assumptions—that a battery with a sufficient range can be produced for $10,000 or less, that he can bring the cost of renewable energy down by committing to buying lots of it, and that the costs of building distributed networks of recharging points and service stations will not spiral out of control.

If he’s right, the cost of powering the electric car will be about 5 cents a mile. As for a gas-powered car, you can do the math, but fuel costs for a car that gets 25 miles to the gallon with gas priced at $3.75 a gallon amount to 15 cents a mile.

Even so, there’s a problem—many people don’t want to pay an extra $10,000 up front for a battery, not knowing how long it will take for them to get their money back in the form of reduced fuel costs. So Agassi isn’t asking for that money up ront. Instead, he intends to sell his customers the cars for much less than they cost, provided that they agree to long-term service plans that will supply them with electricity, battery changes when needed, replacement batteries, etc. He estimates that he could afford to give people a free car if they agree to sign onto a service agreement for six years.

This is the cell phone model—where you get the phone for free or at low cost by signing a long term contract—brought to the auto business.

“We’re AT&T,” Agassi says. “Or Vodacar. All the car companies are the Nokias of the world.”

If all goes according to plan—a huge if—Agassi says that the switch from gas-powered cars to electric cars will be rapid. “You won’t buy a car that depends on gasoline if there is a free car on the market that doesn’t depend on gasoline,” he says.

Clearly, much could go awry with this audacious scheme. Lithium-ion batteries for cars remain unproven technology. Customers need to overcome what the automakers call “range anxiety”—meaning, will people be satisfied with a car that can go only 100 miles without recharging. (Most trips and commutes are far less, of course.) How will customers feel about swapping out their batteries for others during longer trips? And, remember, cars are emotional purchases—the first batch sold in Israel are likely to come in just one or two models, and you won’t be able to select your own color or trim.

And yet—Ghosn is a smart guy, the Israelis are no pushovers, getting the Danes to sign on further ratifies the idea and electric utility companies around the world, which would love to get into the transport business, will be cheering on Project Better Place. Here’s a Business Week article about Shai, and here’s a 25-minute video of his talk last month to a Washington advocacy group called NDN.