The mystery has been solved. In an interview with Rob McNamara for GolfTV, Tiger Woods revealed what gum he is frequently seen chewing on the golf course. 

"Joey (LaCava, Woods' caddie) has this, um, orange, I believe it’s Trident," Woods said. "But I ended up getting hooked on it too because I like the sugar and the flavor, and so that’s what Joey and I end up chewing to wake ourselves up."

Orange Trident gum: added to the grocery list.