Yes when you chew gum it does speed up your metabolism and helps you burn off calories when trying to lose weight.
You can burn off 300 calories if you chew sugarless gum everyday for 4 hours per day and when you chew gum to boost and speed up your metabolism you offset the diminished weight loss that occurs when you eat fewer calories during your dieting.
You need to chew the sugarless gum though for it to have much affect on your metabolism.