Why send a challenge with CHAP? I have been reading about the Challenge-Handshake authentication Protocol (aka CHAP).

Why send a challenge to the user and ask them to hash that challenge with the symmetric key and send that hash back to the server? Why not just ask for a hash value of a symmetric key? And what is the point of this protocol at all when you both have symmetric keys?
The Wikipedia article points out a good reason for using a random challenge value: preventing replay attacks.

If the hash was always the same (as the hash of the symmetric key would be), then having listened in on one challenge-response cycle, a malicious listener could pass further handshake tests.