Within the process of claiming of the Chagos Archipelago by Mauritius, after the decision of the International Tribunal for the Law of Sea and before passing the case to the International Court of Justice and even in the framework of a notification, it would be good to place above all the indigenousness of this peoples so that it can utilize in an effective and efficient manner the Rights of Indigenous People of 2007. Because even if the Law of the Sea constitutes a fundamental point in this claim, that of the Rights of the Indigenous People is even more profound for the people of the Chagos Archipelago. Because it allows without waiting the return of ancestral lands to establish parallel and yet institutional structures. This approach exploits the Rights of Indigenous People in order to transform a question of conscience to an official structure which can represent a peoples not only to claim the rights to international bodies but also to constitute a legislative and executive body in order to manage the rights of its citizens even if they are not yet recognized as official elements of an integral part of a State. This way it avoids the confinement of an inhumane situation and acts catalytically on the process of legal proceedings and this, at all levels so much locally, globally as internationally.