The people of the Chagos Archipelago have been fully expelled and deported to Mauritius and Seychelles by the British government of 1966 to 1973. This deportation had as a purpose, at least in an official manner, to create an open military base to the American army. The problem concerns purely and simply of a spoliation of the right of indigenous people. In reality we can see that this approach had been premeditated and it doesn’t correspond to a result of misunderstanding. Indeed the English government, three months before the independence of Mauritius in 1968 transformed the colony to an amputated Chagos Archipelago thanks to a formal split which allowed it to constitute an overseas British territory, namely the Indian Ocean. This way, it could theoretically be the safeguard of the subsequent claim on the part of Mauritius. Only that, in practice, the Chagos Archipelago people were separated from Mauritius to be better isolated and finally expelled and deported as an entire nation. We therefore have a case which is based on a military research question but which is not incompatible with the existence of an indigenous population and even more of a split which is not of a national sense since it is mostly arbitrary and artificial. Finally there is no opposition on the part of Mauritius for the operation of the base now being American. Also a solution is possible to be set in place.