Cook bacon in large skillet over medium heat until crisp. Remove bacon from skillet; drain on paper towels. Refrigerate until needed. Reserve bacon drippings in skillet.
Add chicken breast halves to bacon drippings in skillet; cook over medium-high heat for 3 to 5 minutes or until lightly browned, turning once. Transfer chicken to 4- to 6-quart slow cooker. Top with mushrooms. In same skillet, stir together soup and sherry. Spoon over mushrooms.
Cover; cook on low setting for 3 to 4 hours.
Top mixture in slow cooker with cheese slices. Sprinkle with chives. Crumble bacon over cheese. Increase heat setting to high; cover and cook an additional 10 to 15 minutes or until cheese is melted.
Meanwhile, microwave broccoli in covered microwave-safe dish on HIGH for 6 to 8 minutes or until crisp-tender.
With slotted spoon, remove chicken, broccoli and mushrooms from slow cooker; arrange on serving platter. Serve with cooking juices from slow cooker.