Combine mushrooms in a 3-1/2 or 4-quart slow cooker; top with chicken breast. Melt butter in a medium saucepan; stir in Italian dressing mix. Stir in mushroom soup, white wine, and cream cheese until melted; pour over chicken.
Cover; cook on low-heat setting for 4 to 5 hours.
Serve chicken and sauce over cooked rice. Sprinkle with chives, if desired. Makes 4 servings.