Preheat oven broiler to 375 degrees F (190 degrees C). Line a broiler pan with aluminum foil. Place chicken on the broiling pan.
Broil chicken breasts in preheated oven for 25 to 35 minutes or until they are cooked through and the juices run clear.
Meanwhile, place mushrooms in a medium skillet, season with salt and pepper to taste, cover skillet and cook over high heat until the juices run. Once that happens, lower heat, remove cover and carry on cooking until liquid has evaporated. Add mushrooms to chicken and sprinkle shredded cheese on top.
Broil for about 8 to 10 minutes, until the cheese is golden and bubbly.
