Preheat the oven to 400°F.
Season the chicken breasts with olive oil, salt, and pepper. Place them in a baking dish.
In a mixing bowl, combine the diced cherry tomatoes, chopped basil, balsamic vinegar, and a pinch of salt and pepper. Stir to combine.
Spoon the tomato mixture evenly over the chicken breasts.
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 the chicken from the oven and sprinkle the shredded mozzarella cheese on top. Return to the oven and bake for an additional 5 minutes, or until the cheese is melted and bubbly.
Drizzle with balsamic glaze if desired before serving.