Preheat oven to 220°C (425°F).

Cook chicken and vegetables: In a large saucepan, combine chicken, carrots, peas, and celery. Cover with water and bring to a boil. Cook for 15 minutes, then drain and set aside.

Make sauce: In another saucepan, melt butter over medium heat. Add chopped onion and cook for 5-7 minutes until soft and translucent.

Stir in flour, salt, pepper, and celery seed until blended, forming a paste-like mixture.

Add liquids: Gradually whisk in chicken broth and milk. Lower heat to medium-low and simmer, stirring frequently, until thickened, about 5-10 minutes. Remove from heat.

Assemble pie: Place the bottom pie crust in a 9-inch pie dish. Add chicken and vegetable mixture. Pour the hot sauce over the top.

Cover with the second pie crust, sealing edges and trimming excess. Cut several small slits in the top crust for steam to escape.

Bake for 30-35 minutes or until crust is golden brown and filling is bubbly.

Let cool for 10 minutes before serving.