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Sprinkle both sides of chicken with 3 teaspoons of the Seasoning. Grill over medium heat 5 to 7 minutes per side or until chicken is cooked through. Cut into bite-size cubes. Mix cheeses, oregano and remaining 1 teaspoon Seasoning in small bowl.
Stretch or roll dough on floured baking sheet to a 12- to 14-inch round, about 1/4-inch thick. Brush top of dough with oil. Place oiled-side down on the grill. Close lid. Grill over medium heat 1 to 2 minutes or until grill marks appear on the bottom of the crust. Carefully flip crust over using tongs or spatula.
Spread tomato sauce on crust. Layer with grilled chicken, cheese mixture, tomato slices, olives and onion. Close lid. Grill 3 to 4 minutes longer or until cheese is melted and crust is browned. (Check pizza often to avoid burning. Rotate pizza, if necessary.) Slide pizza onto baking sheet. Slice and serve immediately.