Whisk vinegar, 2 tablespoons oil, salt, and 1 teaspoon pepper in large bowl. Add chicken and turn pieces to coat all sides. Let sit 10–15 minutes.
Preheat broiler. Arrange chicken on an oiled broiling pan. Sprinkle with remaining 1/2 teaspoon pepper. Broil until cooked through, about 6 minutes.
In a small pan, sauté grape tomatoes in remaining 1/2 tablespoon oil for 3 minutes. Remove chicken from oven and top each piece with a slice of herbed cheese and tomatoes.