Unroll dough, and place on a lightly greased 18- x 12-inch sheet of heavy-duty aluminum foil. Starting at center, press out dough with hands to form a 13- x 9-inch rectangle. Brush dough evenly with olive oil.
Invert dough onto grill cooking grate; peel off foil. Grill, covered with grill lid, over medium heat (300° to 350°) 2 to 3 minutes or until bottom of dough is golden brown. Turn dough over, and grill, covered with grill lid, 1 to 2 minutes or until bottom is set. Carefully remove crust from grill to an aluminum foil-lined baking sheet.
Microwave pizza sauce in a small glass bowl at HIGH 30 seconds or until warm, stirring once. Spread sauce evenly over crust; top with tomatoes and chicken. Sprinkle evenly with cheeses and basil. Return pizza to cooking grate (pizza should slide easily). Grill, covered with grill lid, 3 to 5 more minutes or until crust is done and cheese is melted.