Preheat oven to 400 degrees F (200 degrees C). Lightly grease a medium baking dish.
Bring a saucepan of lightly salted water to a boil. Cook egg noodles in boiling water for 6 to 8 minutes, or until al dente. Drain.
Melt butter in a saucepan over medium-low heat. Mix in flour, heating until bubbly. Slowly whisk in milk. Cook for 5 minutes, stirring constantly, or until thick and smooth. Remove the saucepan from heat. Mix in the noodles, chicken, ham, celery, salt, and pepper. Spoon the mixture into the prepared baking dish.
Bake for 15 minutes in the preheated oven. Sprinkle with cheese and paprika, and continue baking for another 5 minutes. Serve hot!
