Brazilian airlines TAM and Varig, the Chilean LAN and the European Swiss have direct flights to Santiago de Chile from São Paulo’s Guarulhos airport. Aerolíneas Argentinas and GOL have flights with connections in Buenos Aires.
Chilebus has two services per week leaving from Terminal Tietê in São Paulo on Tuesdays and Sundays. The buses leave at 14:30 horas and the trip goes on for 52 endless hours. One way costs R$330 and return is R$627. Airfares have to be way above those prices to make the bus trip worthwhile.
Apparently Pluma travels to Santiago as well, but there are no details on its website.