Preheat oven to 425 degrees.
In a large saucepan or covered skillet, combine chicken, carrots, peas, celery, and onion. Add enough water to cover and boil for 15 minutes.
While you wait, press one of the pie shells into a deep 9 ½ inch pie plate.
Drain the chicken mixture, reserving the cooking liquid. Dump the drained chicken mixture into the prepared pie shell.
Meanwhile in the same saucepan, over medium heat, melt the butter. Add the flour, salt, pepper, and celery seed. Slowly add in 2 cups of the reserved cooking liquid and the milk, stirring well, and continue cooking and stirring until the sauce thickens.
Pour the sauce over the pie filling, then top with the remaining pie shell. Cut some slits in the top to let the steam escape.
Bake, on a cookie sheet, for 30-35 minutes until the crust is golden brown.
Filling will firm up if you wait 10 minutes before serving, but I always cut into it immediately.