LAN, which is one of the largest airlines in South America, currently has some good deals online. Whiel browsing their site, I came across some of these great fares.
* Wed Jan 07 - Wed Jan 14: Miami (MIA) - Buenos Aires (EZE) $826 nonstop, (Air Canada $1,041 w. 1 stop)
* Wed Feb 11 - Wed Feb 18: New York (LGA) - Lima (LIM) $422 w. 1 stop, (Avianca $413 w. 2 stops)
* Thu Feb 19 - Thu Feb 26: Los Angeles (LAX) - Santiago (SCL), $1,082 nonstop (LACSA $988 w 3 stops)
Check out LAN for many other fare options, terms and conditions.