Per The Flight Deal, TAM airlines has some incredible fares to Buenos Aires (via Sao Paulo) in March- June of 2013 from as low as $339 total roundtrip from multiple US cities:
Miami to Santiago, Chile $337 (March 6-11 sample dates): $337 total roundtrip
Miami to Buenos Aires (March 14-17 sample dates): $339 total roundtrip
New York to Buenos Aires (March 9-14 sample dates): $386
Los Angeles to Santiago $350 (sample dates March 7-13)
It seems like these super low fares are only available from New York, Miami and Los Angeles, but if you find any others, feel free to share.
To search flexible dates, I recommend using the ITA matrix calendar- you can enter in dates and how many nights you want to go and it’ll show the dates the low fare is available. One you identify dates, go to whatever online travel site you’d like (I used orbitz.com) and it should let you book- often for cheaper than what shows in ITA.
TAM is currently in Star Alliance, so these fares can be banked to United to earn elite qualifying miles as long as all segments are on TAM. If it includes routing via Lima on LAN, you’ll only be able to bank via TAM or LAN’s programs.
Argentina currently charges US citizens a $160 entry fee, which can be paid in advance here and is good for 10 years.
Chile charges $140 entry fee, good for the life of the passport.
I’ve never been to Santiago, so I’m tempted to book one of these fares. I absolutely love Buenos Aires and have been there before in March and the weather is perfect- hot, but it’s the tail end of summer, so it was bearable. Check out my past stay at the Park Hyatt Buenos Aires and our Destination of the Week: Buenos Aires for trip inspiration!