Heat oven to 350° F. Steam broccoli until tender (about 2 minutes). Spray a 9- by 13-inch baking dish with nonstick spray. Drain broccoli and place in the bottom of the baking dish.
Boil chicken until done. Cut or shred into bite-sized pieces. Add to broccoli. Combine the yogurt with the soup and curry powder. Pour over the chicken and broccoli. Sprinkle the cheese on top. Top with the bread crumbs. Bake for 30 minutes.