Pound chicken breast halves until evenly thin. Dredge chicken with flour. In a large skillet, heat 2 tablespoons of butter over medium heat. Cook chicken in butter for about 4 to 6 minutes on each side, until tender and cooked through. Remove chicken to a shallow baking dish; sprinkle lightly with salt and pepper.
Add 1 tablespoon butter to skillet and sauté mushrooms until tender. Arrange mushroom slices on top of each piece of chicken; cover with a slice of cheese. Place remaining mushrooms around chicken. Place chicken breasts under a hot broiler until cheese is melted. Serve immediately with hot buttered pasta or rice.