United's South America network is a shadow of its former self. Less than ten years ago, United flew nonstop from the U.S. -- mostly MIA
-- to Caracas, Lima, Santiago, Buenos Aires, Sao Paulo and Rio de Janeiro. However, increased competition from other U.S. carriers expanding in the region (namely Continental and Delta) and the continual challenge of having to go up against the 800 lb. gorilla (namely American) which so handely dominates the region, forced United to recede, which was a smart business decision. Today, United has only three daily flights to the region -- daily nonstop service from Chicago and Washington to Sao Paulo, with a connecting flight to Rio de Janeiro, and a daily nonstop flight from Washington to Buenos Aires, continuing on to Montevideo.
If you're trying to get to Santiago and still get United miles, ordinarily you would just fly to GRU
and connect onto a VARIG flight to Santiago. However, with VARIG's present situation, I would never buy a ticket on them for fear I'd lose the value of the ticket, plus lose the reservation itself and have to seek alternative options. In this case, you're best bet is probably to fly Montreal-Miami-Santiago with a single stop on American or fly Montreal-Atlanta-Santiago with a single stop on Delta, although the Delta piece from to Atlanta would be on an RJ
most likely. Or you could always fly on Air Canada via Toronto, and you could still get your Star Alliance miles, but it has a limited schedule and would require a second intermediate stop at Buenos Aires on certain days of the week.