I can't see why we wouldn't be allowed - its sugar-free. But just a word about chewing gum - its not the best when on a diet. Basically, by chewing, you are telling your stomach to expect food and when it doesn't get it, it signals hunger. I actually chew when I'm super-full just to calm things down a bit.
It may be different for you, but just thought I'd mention it if you're having any hunger issues