Heat the oven to 400º F. Carefully peel back the skin of the chicken, leaving one side attached. Season with salt and pepper and lay the sage leaves on the top of the breast, then place the prosciutto on top. Carefully fold the skin over and pat down.
Heat an oven-proof skillet over medium-high heat. Add the oil and when hot, place the breasts skin side down. Cook until nicely browned, then turn and place the skillet in the oven to finish cooking, about 10 minutes more. Slice and serve.