Given the right paint, why not?
Sand it really carefully... I saw people using sandblasters, but if you prefer doing it by hand you can use sandpaper of increasingly fine sandpaper, but never, ever using the coarse one.
A good tip I've read is labeling the joints, like in a puzzle, so you'll know how to put it back.
Of course, you're advised to sand and paint every piece separately.
Here's a good resource, by the way.
http://www.ronhazelton.com/projects/how_to_repair_a_chair_and_restore_it