While gum is popular, its difficult to find one that is organic and made with real ingredients as opposed to made in a lab. You can find better gum at the health food store. Gum made with maple syrup instead of corn syrup, for instance.
Chewing causes your digestive tract to activate as if food is coming. Of course, food is not coming. You body is set to digest but no food is coming so this can have negative effects that may or may not be or become significant.
Chewing gum exposes you and your teeth to more sugar.