How do I prevent water from leaking down my chimney?
Is there a chimney cap? If not, start there. If there is a chimney cap, and it's a brick chimney, odds are you have cracks and/or missing mortar--at which point I'd say your chimney is unsafe...both as a combustion exhaust (you don't want fumes leaking into the house) and as a safety issue (falling bricks hurt). I'd call out a licensed chimney inspector/cleaner/sweep.