Preheat oven to 325 degrees. Simmer chicken lightly in salted water for 25 minutes or until just cooked through. Skin and bone cooked chicken.
Cook broccoli and drain.
Over medium heat, melt butter in a stainless steal, glass, or enamel saucepan. Stir in flour and cook until bubbly. Add broth and Worcestershire sauce. Cook, stirring until thickened. Reduce heat. Stir in 1 cup grated cheese, heating gently until melted.
Empty sour cream into medium bowl. Gradually add cheese sauce, stirring constantly. Add salt to taste.
Arrange broccoli in 8 portions in a 13x9x2-inch baking pan. Top each portion with half a chicken breast. Pour sauce over all. Sprinkle with remaining cheese and paprika.
Bake 20 minutes or until heated through. Brown under broiler, if desired. Makes 8 servings.