Preheat your oven to 375°F (190°C).

In a large bowl, mix the balsamic vinegar, olive oil, minced garlic, salt, and pepper. Add the chicken breasts and coat thoroughly; marinate for at least 30 minutes.

In a separate bowl, combine the diced cherry tomatoes, chopped basil, and a pinch of salt and pepper. Set aside to allow the flavors to meld.

Heat a skillet over medium-high heat. Sear the marinated chicken breasts for about 5 minutes on each side until golden brown.

Transfer the seared chicken to a baking dish. Top each breast with the tomato-basil mixture and sprinkle with mozzarella cheese.

Bake for 20-25 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.

Remove from the oven and allow to rest for 5 minutes before serving.