Is my cat trimming his own claws?

My two year old cat George seems to chew on his claws from time to time. (On his rear paws, as his front was declawed by someone else before we brought him home from the shelter.) We do trim them for him periodically, so I was wondering if it was normal for him to be a nail biter, or if this was a sign that something is wrong?

Yes it's normal. At home I pick up a lot of cat claw trimmings

This is a normal behavior. Cats shed the outer layer of their claws, so at times, they will bite or chew on their claws to help remove the old outer layer. If you have a good scratching post, many times you will find these old claw remnants on the floor near the post.

Or stuck in your foot! OW!