Preheat the oven to 425F and prepare a 9"x13" baking dish by giving it a quick non-stick spray.
Pat down the chicken breasts to remove excess moisture. Wrap each chicken breast with 2 slices of prosciutto each. Place them in the prepared baking dish.
Place the chopped tomatoes and garlic in the baking dish around the chicken breasts and drizzle everything with a little olive oil.
Bake the prepared chicken in the preheated oven for 25-30 minutes, or until the internal temperature of the chicken reaches 165F.
Remove the baking dish from the oven when the chicken is ready. Scoop out the roasted tomates and garlic from the dish and place in a clean bowl.
Add the halved bocconcini balls, finely chopped basil, and balsamic vinegar to the tomatoes. Stir to combine.
Spoon the roasted tomato caprese mixture over the chicken breast when serving.