From the US you have direct non stops daily flights from Los Angeles LAX, Dallas DFW, Miami, and New York JFK. Most of the flights leaves from Miami.
One of the cheapest airlines is AeroContinente, flying from Miami to Santiago. Lan Chile is member of OneWorld alliance, like American Ailines. Traditionally the fares from the West Coast of US and Chile are very expensive. Perhaps the cheapest alternative is to fly to Mexico (in northern hemisphere is low season) and from there to Santiago.
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