Well one Chilean singer I've always liked is Ana Tijoux (she sometimes goes by Anita Tijoux). She does a mix of music like pop R&B, and hip-hop. She's fairly popular, though in terms of overall popularity she's nowhere near the level of some of the international singers like Jesse and Joy, Enrique Iglesias, or Shakira (For a while it was basically impossible to go out in Santiago and not hear either 'bailando' or 'Can't Remember to Forget You').
Back on topic though most of the songs from her newest album "Vengo" are really good and a few songs actually incorporate traditional Andean musical instruments. Anyway a couple songs I'd recommend are:
Somos Sur
Shock
1977