For Chile, we had success with visitchile.com, which is the website of a Chilean travel agency. We booked tickets through them and paid the Chilean resident cost (about 1/3 the US price). Note there was one hiccup where LAN changed the flight time, and because we booked through a travel agency, it was very difficult to get LAN to reaccommodate us to a different time. However, the agency was responsive though there was little they could do.