Preheat the oven to 375 degrees F.

Place the chicken breasts on a sheet pan. Loosen the skin from the meat with your fingers, leaving 1 side attached. Cut the goat cheese into 1/2-inch-thick slices and place 1 or 2 slices plus 1/3 of the julienned sun-dried tomatoes under the skin of each chicken breast. Pull the skin over as much of the meat as possible so the chicken won't dry out. With your fingers, rub each piece with olive oil, and sprinkle them very generously with salt and pepper. Bake the chicken for 35 to 40 minutes, until the skin is lightly browned and the chicken is just cooked through. Serve hot or at room temperature.