How can I quit my gum chewing habit?

Build up willpower. Gum chewing can be a hard habit to quit, because a person is so used to having something in her mouth that she might start eating things. Maybe stopping abruptly and then rewarding oneself with something not related to gum or candy, every 3 days or so, can work. Perhaps one can keep a large bottle of water handy, and take a sip every time she feels the need for something in the mouth.
Switch. If it is sugared gum, switch to sugarless gum. This often causes gas or diarrhea in high doses and that itself will decrease your gum chewing. If it is not causing any dental problems or TMJ pain (pain with chewing), there is not necessarily a reason to reduce it further. Ball players chew gum instead of tobacco, and they make 3 million dollars a year.