Big Red gum does not claim to contain any Xylitol. The ingredients are:
Sugar, Gum Base, Corn Syrup, Natural and Artificial Flavors; Less than 2% of: Glycerol, Soy Lecithin, Color Added, Acesulfame K, Hydroxylated Soy Lecithin, Aspartame, BHT (to Maintain Freshness).
I checked this on the website and the gum pack I have in my hand, they both agree. Big Red is real sugar gum with some added aspartame.