Combine the olive oil, balsamic vinegar, Italian seasoning, garlic, salt, and pepper together in a mixing bowl or a zip top bag. Add the chicken so it’s evenly coated. Let the chicken marinade for at least 1 hour or up to 24 hours.
Remove the chicken from the fridge to have it not be so cold when going on the grill while the grill heats up.
Preheat the grill to medium heat while you make the tomatoes.
In a mixing bowl, add the Roma tomatoes, basil, olive oil, balsamic vinegar, salt, and pepper. Gently toss to combine and let sit while you grill the chicken.
Place the chicken on the grill, close the lid and cook for about 5-6 minutes per side. It’s done when the chicken reaches 165 F.
Remove to a serving plate and top with slices of mozzarella cheese, and 1-2 slices of tomatoes. Sprinkle with more basil slices and drizzle with balsamic glaze, if desired.
Let the chicken rest for 5-10 minutes before serving.