Answer: I'd attack the base of the plant with a vegetation killer such as Round-Up (be careful, it can kill other plants on contact). Once you're sure the parent plant is dead you can begin pulling the vines down from the chimney and the siding. It won't be easy, but once you've gotten the vines down and the roots of the plant killed off, you shouldn't have any more problems with it.
Good luck with your eradication project!
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