There is no hidden or secret way of telling her. If it really bugs you and you want it resolved you can do one of 3 things:
1.) Accept that she has this annoying habbit and learn to live with it…cardinal sin #1 of any relationship is thinking a person will change habbits, personality, etc.
2.) Tell her your concerns. Ask her if there are things that you do that annoy her…make it a mutual “get it all out on the table” discussion. Of course do it lovingly and with compassion. She may not even realize that she does it. She may also have a breathing disorder. I remember reading a while back about how people who chew with their mouth open most likely have trouble breathing through their nose. Watch her when she doesnt have anything in her mouth. If she breaths normally through her mouth rather than her nose, this may be the cause of her annoying habbit. There are other studies that also show that people who have a deep fear of drowining or claustrophobia chew with their mouth open. Again, the restriction of breathing only through the nose can lead to discomfort. However, it is most likely just a case of habbit and a lack of being taught cultured manners.
3.) End it, if it really really bothers you…move on. There are many, many fish in the sea.
BTW: I dated a girl once that always covered her mouth with her right hand while chewing. After the 3rd date it was driving me nuts. I asked her why, and she said it was because she felt the need to keep her mouth open while chewing (the whole breathing through the nose problem stated above) and that she didnt want to be rude. Our relationship lasted about 5 months, but her habbit isnt what broke it off. Eventually I just got used to it.