Heat gas or charcoal grill to medium heat. Cut 14 x 14-inch piece of heavy duty foil; spray foil with cooking spray. Place dough on foil; starting at center press dough to 12-inch round. Place dough on grill, foil side down. Cook, uncovered, 3 minutes or until bottom of crust is light golden brown. Remove from grill.
Meanwhile, in medium bowl, mix artichokes, mayonnaise, red pepper sauce and 1/4 cup of the cheese; set aside.
Using wide spatula, flip crust over on foil so uncooked side is down. Spread artichoke mixture over crust. Top with chicken, bell pepper and remaining cheese.
Place pizza onto grill, foil side down. Cook, covered, an additional 3 to 4 minutes or until crust is golden brown and cheese begins to melt.