Melt butter in a large saucepan over low heat. Stir in the flour and heat until bubbly. Slowly add the milk, stirring constantly, until mixture is thickened and smooth.
Remove from heat and stir in the chicken, ham, noodles, celery, salt and ground black pepper. Transfer this mixture to a 1 1/2 quart casserole dish.
Bake at 400 degrees F (200 degrees C) for 15 minutes. Remove from oven, sprinkle with the cheese and top with paprika, as desired. Return to oven and bake for 5 to 10 minutes, or until cheese is bubbly.
