They were evicted from the British overseas territory in the 1960s to allow the UK government to lease Diego Garcia to the US to use as an airbase.
Many residents of what is the largest of the Chagos Islands ultimately resettled in Crawley, West Sussex.
The petition demands the islanders' right to return home is respected.
TV presenter Ben Fogle, patron of the UK Chagos Support Organisation, handed in the petition, which had been signed by more than 2,500 people.
"Diego Garcia, which is one of the main prohibiters to the islanders returning, is up for renewal in the next year or so," Mr Fogle said.
"We're asking this government to think about whether these islands should belong to the people who inhabited them for a very long time, or to the US government who have used it for renditions - for effectively torture."
He said he had visited the islands and found "houses still as they were left" and "the graveyard strangled by vegetation having been left untended".
"For me, being a Brit, it was probably one of the things I'm most ashamed about, that I'm part of a country that forcibly evicted these people and is now refusing their right to return," he said.
Mr Fogle added: "How wrong is that, that I've been able to be there and they can't?"
Henry Smith, the Conservative MP for Crawley, said: "I think we can't turn back time but what we can do is rectify the problem as soon as possible."
A Foreign Office spokesman said: "The government is committed to its ongoing review of resettlement policy towards the British Indian Ocean Territory."

Hart, 29, is yet to make an appearance for City this season and has been told he can leave the club if he wishes.
"It is a big concern," said Allardyce, who told BBC Radio 5 live he will confirm his captain this month.
But the former Sunderland boss said Hart will be in his squad for next month's World Cup qualifier with Slovakia when it is named on Sunday.
Hart has won 63 caps for England, but had a disappointing Euro 2016, making mistakes against Wales and Iceland as the side was knocked out in the last 16.
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With Hart out of favour with new City manager Pep Guardiola, Argentinian Willy Caballero has been an ever-present for the club so far this season.
Everton are keen on signing Hart, who is not attracted by the prospect of joining interested parties Sevilla and Borussia Dortmund.
Barcelona said on Saturday they had reached the "beginning of an agreement" with City over the transfer of their goalkeeper Claudio Bravo.
"We want as many players as possible in their club's first team that join up with the squad, then go on to play for England and be successful," said Allardyce.
"It doesn't happen as much now as it did 20 or 25 years ago because there are a smaller number of [English] players who play in the Premier League now."
England's opening Group F qualifier for the 2018 World Cup will take place in Trnava on 4 September and will be their first game under Allardyce, who was appointed after Roy Hodgson resigned following the defeat to Iceland.
Allardyce is still to decide whether Manchester United forward Wayne Rooney will continue as captain.
"I will reveal the captain by Wednesday at the latest because everyone is asking the question," he said.
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A petition calling for residents of the Chagos Islands to be allowed to return to their Indian Ocean homeland has been handed in to Downing Street.
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England manager Sam Allardyce is worried about goalkeeper Joe Hart's situation at Manchester City.