Preheat the oven to 400 degrees F/200 degrees C. Cut the mozzarella piece in half, vertically. Slice it in six medium pieces. Take each chicken breast and carve it six times on one side, until you almost reach the other side. In each of the carved spots, place a slice of mozzarella, a slice of cherry tomato and a basil leaf. Sprinkle salt and pepper. Pour the sour cream in a saucepan. Sprinkle fresh dill on the sour cream. Place the two chicken breasts on the sour cream. Cook in the oven for 35 minutes.