I am currently looking at buying a bike in Santiago to travel around South America for a few months. There are scads of new and used bikes to choose from on Chileautos.cl: miles de veh�culos nuevos y usados
You can search by make (marca) or model (modelo) after selecting moto under tipo (type). Then hit the buscar (search) button.
You can check out the prices and see what's available. There is much information on HU if you do a search under buying a bike in Chile. Detailed instructions on getting an RUT. And step by step instructions on the registration process elsewhere on this website.
Reading other peoples blogs I see that the following bikes have held up touring around South America for a few months and are available new in Chile for under 1,250,000 pesos:
Honda CG125 Storm- 899,000 pesos new
Honda CGL125-699,000 pesos new
Euromot GTX200- 950,000 pesos new
I can't recommend a specific bike for you though. Just some possibilities. There are plenty of new and used bikes for sale in Santiago I think you will see after looking at the pages and pages of classified listings.
Honda 125s appear to be the most popular all around bike in South America. Parts availability is excellent. They are bulletproof and dead easy to work on. And have very good resale value at the end of your journey.
Another nice bike is the Honda NXR150 Bros. A sweet little dirt bike with a bullet proof motor. Similar to an XR250 with a smaller motor.
250cc bikes are out of your price range. I have a nice XR250 I bought used for 1500 bucks here in the U.S. Down there it goes for 4,000 +. Yikes. So that means poor people like me are limited to pizza bikes in South America. Oh well. They get 100mpg, so at least I'll save 25 cents in gas going through Venezuela.
Hope this helps