Heat the oil in a 12-inch skillet over medium-high heat. Add the chicken and cook for 10 minutes or until well browned on both sides.
Stir the sauce and 3 tablespoons Parmesan cheese in the skillet. Reduce the heat to low. Cover and cook for 10 minutes or until the chicken is cooked through. Sprinkle with the mozzarella and remaining Parmesan cheese. Let stand for 5 minutes or until the cheese is melted.