While not in Chile, there are some insurance brokers in the US that can provide health insurance for you in Chile. The Long Term Travel Insurance, also known as Expatriate Insurance or ExPat, is travel insurance for people traveling outside the United States for one year or longer. The one plan that I looked into, the underwriter was Lloyds of London. It was called Citizen Secure or International Citizen. Something like that. I don't know how they handle claims and such. I have not chosen a plan yet. For reference the broker that I contacted was called International Corporate Benefits. My insurance broker in the states gave me the contact info for them. They are out of Atlanta, but you might get an idea of the costs involved.
http://www.internationalcorpben.com/index.html