The effect of teeth whitening was discovered quite by accident. In the past, dentists tried to treat gum disease with mouth rinses containing hydrogen peroxide. They noticed teeth became whiter over time following use of these mouthwashes.
Are you only an occasional gum chewer? If so, and you figure it can't hurt to pick up a pack of "whitening" gum, you should know that your teeth won't get any whiter unless you're constantly chewing the stuff.