He moves his head from left to right frequently with a chewing motion. I
know it is hard to explain but I'll try ...

Imagine a human vigourously chewing gum and at the same time nodding his
head.

Without more information on the cat, I can't say much about whether
this idea really has any merit, but when I read the subject line, it
reminded me immidiately of "bruxism" (teeth grinding), which is listed as
one of the side effects of Prozac, and other psychotropic medications.
This seems unlikely, but it is possible that the cause is psychogenic.

Disclaimer: I'm not a vet, or a pet psychiatrist (if those really exist
yet).

Jim