Sauté mushrooms in butter or margarine for 3 minutes and set aside. In a small bowl, combine the lime juice and olive oil. Dip each chicken part in the mixture, covering completely. On an aluminum foil-lined baking pan, arrange the chicken in a single layer. Sprinkle with salt and pepper. Broil one side for 15 minutes, then flip the chicken and dress with the remaining lime and oil mixture. Broil for an additional 15 minutes, or until you can easily insert a fork into the chicken. Take the dish out of the oven and pour the mushrooms over the chicken. Return to the oven for about 2 minutes.