Preheat oven to 425°F (220°C).
In a saucepan, add the chicken breasts, carrots, green peas, and celery. Fill with enough water to cover the ingredients. Cover and boil for 15 minutes. Remove the pan from heat, drain, and reserve.
In a large pan, cook leeks with butter over medium heat until translucent. Add the flour, salt, pepper, and celery seeds. Stir in the chicken broth and milk. Simmer over medium-high heat until the mixture thickens. Reserve.
Pour the chicken and vegetable mixture into the first crust-lined pan. Pour hot liquid mixture over. Top with the second pie crust, seal the edges, flute, and cut off the excess dough. Cut slits down the center of the top crust in several places for the filling to vent and steam to escape.
Bake for 30 to 35 minutes or until the crust is golden brown and the pie mixture is boiling. Let stand for 10 minutes before serving.