Make a slit with a knife along one side of each breast. Cut about an inch from the other side to make a pocket. Divide the cheese and stuff equally into each pocket. Insert 2-3 basil leaves into each pocket. Season the breasts with salt and pepper. Heat the oil in a large non-stick skillet over medium-high heat. Add breasts to the skillet and cook for about 20 minutes, turning several times until chicken is browned and cooked through. Serve immediately.