If you are one of those ultra-rich people, why would you settle for mere vacation homes situated on some hill when you can buy your own private island? Yeah, what could be more private and relaxing than having your own piece of land, isolated from all civility?
Here is a list of private islands for sale in Chile. Beware, though. They are not cheap. Prices start at a one million dollars. Who cares about the price if you're ultra-rich anyway?