Preheat oven to 350 degrees F (175 degrees C).
Boil chicken until tender and shred or cut into bite size pieces. Meanwhile, steam broccoli until crisp but tender.
In a small bowl mix together the soup and mayonnaise. Set aside. In a 9×13 inch baking dish layer the chicken, broccoli, soup mixture, and cheese. Sprinkle dry stuffing mix over the top and bake in the preheated oven for 25-30 minutes