Sprinkle surface of chicken with salt and pepper; brown on all sides in butter in a large skillet. Remove chicken from skillet, and set aside.
Sauté shallots in butter in skillet until tender. Return chicken breasts to skillet; add wine. Cover and cook over low heat 20 minutes. Add mushrooms and chopped parsley; cover and continue cooking 5 minutes or until chicken is tender. Remove chicken to a warm serving platter; spoon mushroom sauce over chicken and serve.