While Rapa Nui [1] is administratively subject to Region V ( Valparaíso), with a governor (usually a local) appointed from Santiago, it is also a separate municipality with an elected mayor.
The current local administration distrusts both the central and regional governments, resents the inability to raise revenue locally, and argues that islanders should have autonomy within the Chilean state. Dissenters, though, argue that recognition as a separate people means second-class citizenship. Land rights also continue to be a hot issue, as some oppose government “grants” on the rationale that Chile cannot give away what it never rightfully acquired.
Links:
[1] http://www.moon.com/destinations/chile/-chilean-pacific-islands/rapa-nui-easter-island