In a large bowl whisk together the cherry tomato sauce, olive oil, Italian seasoning, salt and pepper. Place the pounded chicken breasts in a freezer bag and pour the mixture over the breasts. Squeeze the air out of the bag, seal and refrigerate for at least 2 hours, turning occasionally.

Heat the grill to at least 400 degrees F. Drain the marinade from the chicken and reserve for brushing. Place the chicken on the grates, brush the top with the marinade, cover and cook for 4-5 minutes. Turn and brush again. Cover and cook for an additional 4 minutes. Turn and brush again. Continue cooking and turning until a meat thermometer place in the thickest part of each breast registers 160 degrees. Place the basil leaves on top of each breast, followed by the mozzarella cheese (press down lightly on them if using the pearls). Lightly brush over the cheese with the marinade. Cover and cook for a few minutes more, until the cheese is melted and the chicken is at least 165 degrees.