The INC has long been the most visible Iraqi exile group, and Chalabi, a wealthy businessman based in London, has been lobbying the United States for years in an attempt to force Saddam Hussein out.
But Chalabi has his enemies. Officials at the State Department and the CIA are working hard to keep him out of power. They call him an unreliable opportunist who misled the Bush administration into thinking that the war would be a cakewalk.
For now, however, Chalabi has come home. He hopes for good. We found him, surrounded by bodyguards, operating from a fortified complex in the Kurdish-controlled mountains of northeastern Iraq.
He's in constant contact with U.S. military commanders and politicians, trying to push his organization front and center in the power struggle over who should run post-war Iraq.
"The U.S. government has decided that there should be an interim Iraqi authority which will be selected by the opposition," says Chalabi. "This is not an American-formed authority. "It is composed of Iraqis, not Americans."
"The talk of a military government has stopped. Instead we have an Iraqi interim authority which will take over immediately after liberation."
But Chalabi's wrong.
They won't call it that, but there will be a U.S. military government. And while President Bush has decided to create an Iraqi authority, he hasn't decided when -- or who -- will be in it.
At first, retired U.S. Air Force General Jay Garner will run Iraq, along with other high-profile Americans. We've also heard that they're talking about having people like Jim Woolsey, a former CIA director, to run the Ministry of Information – along with other Americans who will run the departments.
But Chalabi says that isn't going to happen.
"Jim Woolsey's a great man. We like him very much. But I think the people are discovering very quickly that Iraq is not Afghanistan," says Chalabi. "You cannot buy people. The Iraqi people have to feel that their leadership must be seen to play an important role in this process of liberation."
That sounded to us like someone who might see himself as Iraq's next president, but Chalabi insists this will not happen.
"I'm not a candidate for any position in Iraq, and I don't seek an office," he says. "I think my role ends with the liberation of the country."
Most people don't believe him. But the idea of his having any role in the next Iraqi administration sparks passionate debate.
Martin Indyk, of the Brookings Institution, was in charge of U.S. - Iraq policy during the Clinton administration.
"I think the Pentagon intends to have a role for him, but the danger here is that Ahmed has no support inside Iraq, and he has very little support outside Iraq," says Indyk.
"The other opposition people don't support him, and won't follow him. And so if we try to impose Chalabi on the Iraqi people we will just be reinforcing their image of an outside power determined to have our way."
Chalabi's supporters say Iraq needs an exile like him precisely because he understands how democracy works.
Dressed more like a lobbyist than a freedom fighter, Chalabi spent years pushing the U.S. government to go after Saddam Hussein. We were with him last year as he took his "Invade Iraq" message to Capitol Hill and the Pentagon.
Those visits are paying off now. The Pentagon is backing him. The CIA, on the other hand, is fighting him tooth and nail.
According to sources from the Bush administration, the CIA has been circulating a dossier this week that blames Chalabi for providing the U.S. with woefully inaccurate and overly optimistic intelligence about how Iraqis would react to an invasion -- charges Chalabi now denies.
In an interview last year, Chalabi said that "the army will not fight to defend Saddam, and in fact, they will defect willingly."
"That is true. The army did not fight to defend Saddam," says Chalabi, in reference to his statement last year. "The Marines and the U.S. Third Division cut like knife through butter through two divisions of the Republican Guard near Baghdad in less than 24 hours."
Chalabi also predicted there would be a popular uprising, when the American Army came in. But so far, this really hasn't happened.
"The U.S. government publicly asked the Iraqi people not to do an uprising," he says. "U.S. officials told opposition leaders specifically "no uprising." They asked them to stay at home when military operations were going on."
But that doesn't explain why so many Iraqis were hostile to U.S. forces. The Pentagon listened to Chalabi's assurances that Iraqis would embrace our soldiers as the invasion began.
Instead, they were shot at by Saddam's Fedayeen militia.
Chalabi certainly didn't tell Americans that the Ba'ath party would have this kind of power, that there would be the Fedayeen to fight. Instead, he said it would be a cakewalk.
Chalabi, however, denies that. He claims that he described the Fedayeen organization in detail, but his reports were not taken seriously.
"They did not expect what they faced in the south, but not because of us," says Chalabi. "There have been agencies of the U.S. government who have spent many millions, tens of millions of dollars if not more, on trying to buy information and buy people in the south. All these funds were spent to no good effect."
Instead, Chalabi is blaming his nemesis, the CIA. He says their faulty intelligence, not his, led war planners astray. And now they're trying to divert attention from that failure by campaigning against him.
"It is surprising to me that the CIA would have time to engage in such activities when they should be focusing on Saddam," he says. "It seems to me they are more focused on me than on Saddam at this time."
But there's little doubt that Chalabi's message was "Saddam's defenses will come apart like an old suitcase" -- and that administration hawks paid attention.
Just before the shooting started, Vice President Cheney said that it was meetings with and information from Chalabi's organization that led him to this conclusion: "The read we get on the people of Iraq is there's no question but what they want to get rid of Saddam Hussein and they will welcome as liberators the United States when we come to do that."
During Indyk's management of Iraqi policy during the Clinton years, he says that he trusted, but always verified, information provided by Chalabi and his group.
"We had reason to admire Ahmed," says Indyk. "He was courageous. He was fighting for a cause against a very evil man, and there weren't too many Ahmed Chalabi's around."
But does Indyk think Chalabi was getting faulty intelligence out of Iraq, or that he deliberately misrepresented it so he'd get U.S. support?
"He wanted to bring Saddam Hussein down," says Indyk. "He had an interest in convincing us of the need to go and do that, and that it could be done relatively easily. It's not Chalabi's fault that he was trying to sell us a bill of goods, and that we bought it."
It is possible that Chalabi was right -- that Saddam's forces will collapse completely and the people will welcome us after all. But he doesn't think U.S. soldiers should make their reservations home just yet.
"The American military should stay in Iraq until the first elections are held and a democratic government is established," Chalabi says. "I'm not prepared to give a time frame, but we expect to have a constitution ratified within two years."