Preheat the oven to 400°F.
Season the chicken breasts with olive oil, salt, and pepper. Place them in a baking dish.
In a bowl, combine the diced cherry tomatoes, chopped basil, minced garlic, balsamic vinegar, and red pepper flakes (if using). Stir well to combine.
Spoon the tomato mixture evenly over the chicken breasts.
Sprinkle the shredded mozzarella cheese on top of the tomato mixture.
Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove from the oven and let it rest for 5 minutes before serving.