Preheat oven to 425°F
Melt 1/3 cup butter in a saucepan
Add 1/3 cup chopped onion and cook until soft
Stir in 1/3 cup all-purpose flour, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/4 teaspoon celery seed
Slowly whisk in 1 3/4 cups chicken broth and 2/3 cup milk
Cook until thick and bubbly
Stir in 2 cups cooked chicken and 1 1/2 cups mixed vegetables
Remove from heat
Place one pie crust in a 9-inch pie dish
Pour the chicken filling into the crust
Cover with the second pie crust
Seal and crimp the edges
Cut slits in the top crust
Bake for 30 to 35 minutes until golden brown
Let stand for 10 minutes before serving