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Place chicken in large resealable plastic bag or glass dish. Add 1/2 cup of the marinade; turn to coat well. Reserve remaining marinade for brushing. Refrigerate chicken 30 minutes or longer for extra flavor. Remove chicken from marinade. Discard remaining marinade.
Grill over medium heat 5 to 7 minutes per side or until cooked through, brushing with 1/4 cup of the reserved marinade. Cut chicken into bite-size cubes.
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.
Brush crust with remaining 1/4 cup marinade. Layer crust with 1/2 of the cheese, grilled chicken, tomatoes and remaining cheese. 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. Sprinkle with cilantro, if desired. Slice and serve immediately.