Preheat your oven to 375°F (190°C). Spray a baking dish with cooking spray or lightly coat with olive oil.
Place the chicken breasts between two pieces of plastic wrap or parchment paper. Use a meat mallet or rolling pin to gently pound the breasts to an even thickness, about ½ inch thick.
In a mixing bowl, whisk together the balsamic vinegar, olive oil, minced garlic, dried basil, dried oregano, salt, and pepper until well combined.
Place the chicken breasts in the prepared baking dish and pour the balsamic mixture over the top, ensuring the chicken is well coated.
Bake in the preheated oven for 25 minutes.
After 25 minutes, remove the baking dish from the oven and arrange the mozzarella cheese slices on top of each chicken breast.
Return the dish to the oven and bake for an additional 5-10 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let it rest for a few minutes before serving. Garnish with fresh basil leaves if desired.