The US says resettlement would harm the security of Diego Garcia
Thousands of Chagos Islanders will learn later whether the government can stop them returning to their homes.
Some 2,000 residents were forced out when the British colony in the Indian Ocean was leased to the US in the 1960s to build an airbase at Diego Garcia.
The Court of Appeal has ruled that they do have the right to return, but the government is challenging that decision in the House of Lords.
The Law Lords will make their final judgement on Wednesday morning.
Many former residents of the Chagos now live in Mauritius or the UK, but most are desperate to return home.
The US has argued, however, that any resettlement could compromise the security of Diego Garcia which was used to launch bombing missions on Afghanistan and Iraq.
In 2000, the courts ruled that Chagossians could return to their homes in 65 of the islands, but not to Diego Garcia.
But in 2004, the government used the royal prerogative to effectively nullify the decision.
In 2006, the High Court overturned that order - a decision which the Foreign Office then took to the Court of Appeal.
The judges said at the time: "The suggestion that a minister can, through the means of an Order in Council, exile a whole population from a British overseas territory and claim that he is doing so for the 'peace, order and good government' of the territory is, to us, repugnant."
In 2007, the Court of Appeal again ruled in the islanders' favour, but the government was granted leave to appeal on the condition that it agreed to pay the legal costs.