Preheat oven to 425 degrees F (220 degrees C).

In a medium saucepan, combine chicken, carrots, peas, and celery. Add water to cover and boil for 15 minutes, then drain and set aside.

In the same saucepan over medium heat, melt butter and cook onion until translucent.

Whisk in flour, salt, black pepper, and celery seed until well combined.

Gradually whisk in chicken broth and milk, simmering until the sauce has thickened.

Place the cooked chicken and vegetable mixture into the bottom pie crust.

Pour the sauce over the chicken and vegetables.

Cover with the top pie crust, seal the edges, and cut small slits in the top crust to allow steam to escape.

Bake for 30 to 35 minutes until the pastry is golden brown and the filling is bubbly.

Allow the pie to cool for 10 minutes before slicing and serving to allow the filling to set.