Slice the breasts nearly in half lengthwise, so they are still attached. Stuff each with 4 marinated tomatoes, 4 basil leaves and 3 large slices of mozzarella. Brush each breast with oil, vinegar and salt. Secure the chicken with two toothpicks.
Preheat the oven to 400 degrees. Heat a large skillet on medium-high and add prepared chicken. Cook on each side until golden and seared. Bake for 10 to 15 minutes until cheese is melted and the chicken reaches 165 degrees. Serve immediately.