Doesn't belong to the US. It's British Indian Ocean Territory.
Indeed it is.
Unfortuanately for the people that lived there for 3 or 4 generations it is no longer their home.
Britain did not have use for it as a trading outpost/stopping point so did a deal with the US.
The people that had called it home for over a century were forcibly deported and moved to a slum in Mauritius where they live in poverty to this day.
Government after government have ignored their plight and refused help to these people.
It is a very sad story.