Easy battle to win - http://shop.wbu.com/p/wbu-fundamentals-squirrel-proof-bird-f...

I have been using this feeder for something like 7 years and barring really weird circumstances, it is 99% effective. And no they cannot chew through it.

Combine this with a baffle - http://shop.wbu.com/p/wbu-aps-squirrel-baffle and you will be as close to 100% effective as possible. Barring squirrels suicide leaping from trees, which I would not put past them.