Heat milk and cream cheese cubes over low heat, stir until smooth. Stir in the Worcestershire sauce.
Place broccoli in a 10 x 6-inch baking dish. Top with 1/2 cup of cheddar cheese, break chicken into pieces and pour cream cheese sauce. Cover with foil.
Bake for 25 minutes. Remove from oven and sprinkle the remaining 1/4 cup Cheddar cheese and bake until Cheddar cheese is melted - approximately 5 minutes.