Today La Tercera newspaper says that persons on short term visas and persons with RUT can sign up for Fonasa health insurance. I would investigate that if you have to health insurance.
If you go to the hospital here without insurance you can find yourself in debt for $10,000 and then blacklisted by Dicom.
Someone from an Isapres wrote here on Internations that foreigners can get Isapres private health insurance. I find that claim doubtful. I took numerous physical exams before I was able to get Isapres insurance.
I wrote something here explaining the whole insurance and medical system Protected content