The Americans had asked the British, their longtime allies, who still had colonies in the region, to find an uninhabited island for their base.
There was just one problem -- there were inhabitants on Diego Garcia and they have been living there for more than 200 years. Correspondent Christiane Amanpour reports.
But the British didn't see that as a problem. They simply moved all the inhabitants 1,200 miles away to other tropical islands, Mauritius and the Seychelles.
Back then when the island was a British colony, Marcel Moulinie managed the coconut plantation. He was ordered to ship the people out.
"Total evacuation. They wanted no indigenous people there," says Moulinie.
"When the final time came and the ships were chartered, they weren't allowed to take anything with them except a suitcase of their clothes. The ships were small and they could take nothing else, no furniture, nothing."
The people of Diego Garcia say they left paradise and landed in hell when they were dumped here in the urban slums of Mauritius. They had brought no possessions and as islanders who had lived off fishing and farming they had no real professional skills.
No one helped them resettle or pay for the homes they lost. They were forced to become squatters in a foreign land.
Before the final evacuation, the British had cut off the ships carrying food and medicine to Diego Garcia.
Jeannette Alexis' family was one of the last to leave: "My father was told that we had to leave the island because the Americans were moving in and it wasn't safe to remain on the island anymore."
The islanders say the other force that got them out was fear when British officials ordered their pets to be exterminated. They were gassed with exhaust fumes from American military vehicles.
"You can imagine the pressure it put on the population there," says Alexis.
"We were crying, we were hanging onto our mothers' skirts crying, because although we were very young we understood that we were leaving something very valuable behind, and that was our home."
And for the next 30 years, the world never knew what happened to Diego Garcia's original people.
No outsiders are allowed onto Diego Garcia, so this secret stayed hidden until one of the exiled islanders, Olivier Bancoult, started organizing his community.
Bancoult was angry by the years of misery his people were forced to endure. Three of his own brothers drank themselves to death, dispirited by their poverty and unemployment. And one sister was so homesick she committed suicide.
"That's very sad, that's why I will never give up," says Bancoult. "All the difficulty is because of U.S. and UK, they turned peoples' life into a nightmare."
So three years ago, Olivier traveled to London to take the British government to court. His big break came when he and his lawyer, Richard Gifford, found secret documents that had recently been declassified that described the agreement between the United States and British governments to build the base on Diego Garcia.
"Here we have the legal expert in the foreign office, in which he's got a paragraph headed, maintaining the fiction," says Gifford, referring to the fiction that Diego Garcia had no native people.
These British documents reveal that colonial officials thought no one would notice if they deported the islanders.
"I find it rather shameful, yes," says Gifford. "Here we have an interesting memorandum of the British Government: There will be no indigenous population except seagulls."
Another British document confirms that "evicting the people and leaving the island to the seagulls" was done at the request of the United States. It reads: "The United States Government will require the removal of the entire population of the atoll by July."
"And the British were only too happy to oblige," says Gifford.
What did the British get in return for providing the Americans a population-free island? Polaris missiles for their submarines. The U.S. reduced the price by $14 million dollars, or $5 million British pounds.
"So five million pounds was a massive incentive compared with a very modest conscience problem," says Gifford.
Uncovering the paper trail brought Gifford and Bancoult a stunning victory. Britain's highest court ruled that deporting Diego Garcia's native population was illegal.
But the euphoria didn't last long because the court didn't propose a remedy -- neither money nor what the people wanted most - to return home and have the right to earn a living on the base.
"The position of the islanders is that they never objected to the U.S. base on Diego, but the islanders are extremely bitter that they are denied employment on the base. Precisely because they come from there," says Gifford.
The base currently employs several thousand civilian workers from other countries like the Philippines - and they don't want visitors. When the islanders asked to visit their family graves, they were told from the British government that the U.S. had to grand permission.
So last August, the islanders appealed directly to President Bush. The Bush administration, however, said it was Britain's call: "Because of the vital role the facility plays in the global war on terrorism, British authorities have denied permission to visit Diego Garcia. We concur and support the decision."
Caseem Uteem, the former president of Mauritius, had written the letter to President Bush on behalf of the islanders. He believes that both sides are passing the buck.
"That's what they're doing," says Uteem. "I think it is not only inhuman but illegal. They should never have expelled them from their land."
Neither the British nor the U.S. governments would talk to 60 Minutes about the issue, but the former commander of the base on Diego Garcia spoke to Amanpour.
"I have a great sympathy for them," says Dan Urish. "I think the British are probably legally responsible for it. Morally, the U.S. certainly has an interest in seeing that things are made right for the islanders."
Until that happens, Olivier Bancoult, Jeannette Alexis and the rest of the islanders say they will never give up. Now they are suing both the U.S. and British Governments for compensation and the right to return.
"It's an important base, I agree, but at the same time they should have realized that people are also important," says Alexis.
"The Americans and the British always talk about the champions of human rights. What they did to us they should rectify, they should look after us. You know, they should do what they preach."