Place chicken breasts in a large resealable plastic freezer bag, one at a time. Lightly pound chicken breasts to an even thickness of about 3/4-inch. Combine oil, balsamic vinegar, garlic, Italian herb seasoning, salt and pepper in a small bowl and whisk until combined. Pour half of the marinade over the chicken, reseal bag, and set aside to marinate for at least 15 minutes. (Chicken and marinade can be prepared ahead; covered and refrigerated overnight.)Advertisement
Preheat grill to medium heat or about 350 degrees F. Combine remaining marinade with diced tomatoes and red onion; set aside. Transfer chicken from marinade onto grill surface and discard marinade. Grill chicken for 4 to 6 minutes per side or until cooked through. Transfer the chicken to a serving plate and sprinkle with shredded cheese. Spoon bruschetta mixture over chicken and top with basil; serve immediately.