American Airlines has Los Angeles LAX to GIG Rio de Janeiro, Brazil at $645 round trip for nearly every date from October 6 to December 3, even Thanksgiving week.
Looks like a 3-day advance purchase and 3-day minimum stay from date of departure. This is a high mileage low fare for American AAdvantage flyers possibly wanting to reach a higher elite status for 2016.
Routing via Miami Airport makes the round trip flight distance 13,009 miles.
American Airlines Los Angeles LAX – Miami MIA – Rio de Janeiro GIG
$644.33 Wednesday November 11 – Saturday November 14
Flight distance: 13,009 miles
This mileage run flight schedule with a Wednesday noon departure from LAX and Thursday early morning arrival in Rio makes the trip possible with only one hotel night. The departure back to Miami is 1:15am Saturday morning. No hotel night required for Friday night before flying back.
Aeromexico has fares in the mid-$500s to many airports in Brazil during this same season. American Airlines has similar fares in mid-$600s to Sao Paulo GRU. American and TAM have fares in the mid-$600s to numerous airports around Brazil available through TAM website.