In a small bowl, whisk together the marinade ingredients. Place the chicken in a resealable plastic bag or shallow dish and pour the marinade over it. Refrigerate for at least 1 hour or up to 24 hours before assembly. When ready to cook, remove the chicken from the marinade and discard it.
Preheat your oven to 400℉. Prepare your baking sheet by spraying a rimmed baking sheet lined with foil with non-stick cooking spray.
Place each chicken breast flat on a cutting board. Make four deep cuts about ½ inch apart across each chicken breast without cutting all the way through.
Fill each cut with slices of tomato, mozzarella, and basil leaves.
Place the stuffed chicken on the prepared pan and bake for 25–30 minutes or until an instant-read thermometer inserted into the thickest part of the breast reaches 165℉.
Once baked, remove the chicken from the oven and allow it to rest for about five minutes. Drizzle with balsamic glaze if using and garnish with extra chopped basil before serving.