The US base has been established since 1971, but the rest of the Chagos are unpopulated. Mauritius maintains a claim on the Chagos based on the fact that in colonial times the barely inhabited archipelago was administered from there although the islands are geographically closer to India. India put in claims for the Maldives and Andaman Islands in 1947--the Maldive claim was ignored (the place was a protectorate) and India eventually got the Andamans in 1950. India ha a very big naval presence in the Indian Ocean (where else?) an regularly shows the flag at the Indian Ocean islands. Practically they would not take on the US, but sovereignty doesn't mean a lease could not remain--it was due to expire in 2016 anyway.