In general, signing up for a travel-insurance policy is a good idea. For Chile, a basic theft/loss and medical policy is recommended. Read the fine print carefully because some companies exclude dangerous activities from coverage, which can include scuba diving, motorcycling, and even trekking. You may prefer a policy that pays doctors or hospitals directly rather than you having to pay on the spot and make a claim later.
Make copies of all insurance information in the event that the original is lost.