In a medium sized bowl, whisk together olive oil, red wine vinegar, garlic powder, onion powder, Italian seasoning, kosher salt, and black pepper. Coat chicken breasts and marinate for 15 minutes.
Preheat oven to 400℉ and adjust oven rack to upper third of oven. On an 18x13 sheet pan, toss cherry tomatoes with olive oil, garlic powder, kosher salt, and pepper. Arrange tomatoes around edge of sheet pan and place chicken breasts in center. Season chicken breasts lightly with additional salt and pepper.
Bake chicken and tomatoes for 20 minutes, or until internal temperature of chicken is just shy of 165℉. Remove from oven and top with mozzarella and a drizzle of balsamic glaze. Turn on oven broiler and broil chicken for 3-5 minutes, watching to make sure it doesn't burn. Once cheese is melted sprinkle with fresh basil and serve.
