Marinate chicken in Italian dressing for several hours, or overnight.
Preheat grill. Grill the chicken on each side until it’s cooked all the way through.
Coat one side of a piece of aluminum foil in cooking spray. Place foil onto grill, with the side coated in cooking spray facing up.
Transfer the chicken to the aluminum foil. Top each piece with mozzarella, tomato slices, and 2-3 leaves basil. Drizzle with balsamic vinegar. Close the grill lid and cook for a few minutes, allowing the cheese to melt.
Transfer to plates or serving platter. Garnish with remaining fresh basil. Drizzle with more balsamic vinegar if desired.
Stand away from the grill when coating the foil with cooking spray. Keep cooking spray can away from the grill's heat.