In a bowl, whisk together the sauce ingredients. Season with salt and pepper, to taste. Set aside.
In a separate bowl, toss together the tomatoes, mozzarella, and basil. Season with salt and pepper, to taste. Set aside.
Preheat oven to 400 degrees F.
Heat oil over medium-high heat in a large oven-safe skillet. Season the chicken all over with salt and pepper, to taste. When the pan is hot and oil is shimmering, add the chicken to the skillet in a single layer. Cook for 1-2 minutes on each side or until lightly golden brown. Add the balsamic sauce mixture. It should quickly come to a simmer. Use a wooden spoon to scrape up any brown bits from the bottom of the pan.
Immediately remove the pan from the heat and add the tomato mozzarella mixture over the chicken.
Bake uncovered for 18-23 minutes or until chicken is fully cooked through. Internal temperature should register at 165F. Remove from the oven and rest for 5 minutes before serving.