
Whisk together 2 tablespoons of olive oil, garlic, Italian seasoning, salt, and ground black pepper in a medium bowl. Add the chicken breasts and mix gently to coat. Cover and refrigerate for 30 minutes.
Combine the tomatoes, garlic, balsamic vinegar, salt, and black pepper in a medium bowl. Set aside to marinate as you cook the chicken.
Heat a large skillet over medium heat. Add the remaining tablespoon of olive oil. Place the marinated chicken in a single layer and cook for 5 to 7 minutes or until golden brown on the bottom.
Flip the chicken breasts and continue to cook for an additional 5 minutes or until golden brown and the internal temperature of the chicken reaches 155°F. Top each piece of chicken with a slice of fresh mozzarella, cover, and reduce the heat to medium-low. Cook until the cheese is melted and the internal temperature of the chicken has reached 165°F, about 3 more minutes.
Stir the basil into the topping. Serve each piece of chicken topped with the tomato mixture and an extra drizzle of balsamic glaze.