From National Geographic
http://news.nationalgeographic.com/news/2006/06/060613-cat-bear.html The site is in New Jersey. They say the cat, who weighs 15 pounds and is declawed, really did chase the bear up the tree. Not only that, but when the bear tried to escape after 15 minutes or so, the cat chased it up another tree.
Obviously, it's all a matter of attitude. No firearms required.