Pour 1/4 cup dressing over chicken in large shallow nonaluminum baking dish or plastic bag. Cover or close bag and marinate in refrigerator, turning occasionally, 30 minutes or up to 3 hours.
Remove chicken from marinade, discarding marinade. Grill chicken, turning once and brushing frequently with an additional ¼ cup dressing, until chicken is done. Grill tomato slices, brushing with dressing, turning once until just softened.
Thinly slice chicken breast. Arrange tomato slices on top of chicken and top tomato with burrata. Garnish with basil leaves and freshly ground black pepper. Drizzle, if desired, with additional dressing.