Is it possible to open a bank account in Chile with with US dollars as currency?
As suggested in the comment to your question, the first place to go is a bank, and ask them "Can I open an account in USD please?". The answer might vary, depending on the banking regulations, but they WILL have an answer for you.
(As an aside, some countries are more strict than others regarding the opening of bank accounts. Where I live you can only usually open a bank account if you have a work permit. I am not sure if Chile is as strict as that though.)