Based on the age of this post, you've probably already finished...but just in case:
I used an Osprey Airporter duffel bag. It's designed to contain your backpack so nothing gets loose and your buckles/straps don't get caught in the baggage claim treadmill. The Airporter can swallow all but the hugest packs, has a shoulder strap, and an ID card holder. When not in use, it folds down to a little smaller and thicker than a frisbee. Price: about 30 bucks (US).
But, keep in mind that you'll either have to haul it around with you, or mail it on to Santiago for later pick-up (as I did with mine). And as others have said, you can get away with a heavy-duty garbage bag.