My program allows it. They do warn that it might make you swallow air. This is true pre-op as well. I used to chew gum when I was hungry but I've since developed tmj and can't do it anymore.
That's funny that you mentioned TMJ, I had/have a severely bad case of this prior to surgery, after my surgery it seemed like a miracle had happened and I no longer suffer from this, at least not in the past 6 months, knock on wood!