Melt 2 tablespoons butter in large skillet over medium heat. Add chicken breasts; cook chicken 12 to 15 minutes or until fork tender and juices run clear, turning once. Remove chicken from skillet; keep warm.
Melt 2 tablespoons butter in same skillet; add mushrooms and onion. Cook until vegetables are tender, stirring occasionally. Season with salt and pepper. Add sherry; bring to a boil. In small bowl, combine milk and cornstarch; blend well. Add to mushroom mixture; cook until mixture thickens and boils.