Boil chicken, carrots, peas, and celery for 15 minutes. Drain and set aside.
In a saucepan, sauté onions in butter. Stir in flour, salt, pepper, and celery seed.
Slowly add chicken broth and milk. Cook until thick and bubbly.
Stir in the chicken and veggies to combine.
Place one pie crust in a 9-inch pie dish, fill with the mixture.
Cover with the second crust, seal edges, and cut small slits in the top.
Bake at 425°F (220°C) for 30-35 minutes or until golden brown.
Cool for 10 minutes before serving.