Chicha is pretty much a cottage industry, you'll find Argentinean sidra in champagne-style bottles in Lider, but not the Chilean sort I think. You'll probably have more luck finding chicha in a frutería / verdurería or a local market. Or if you have friends in the south maybe they can ship some north with Turbus... in coke bottles it seems to be pretty robust in spite of all the gas.
I've enjoyed a few bottles since I got here

You are disturbing me. I am picking mushrooms.