Coat a large slow cooker with cooking spray, and place chicken breasts into an even layer onto bottom of crockpot.
Layer sliced onion on top of chicken, and sprinkle with onion soup mix.
Pour French onion soup over top, and place lid onto slow cooker.
Cover and cook on low 8 hours or on high 4 hours.
Preheat broiler, and coat baking dish with cooking spray.
Place chicken breasts into baking dish, and add about 1/2 cup broth into the dish.
Top with chicken breast with the cooked onion and a slice of Swiss chese.
Broil until melted and bubbling, about 2 minutes. Serve immediately.