In a large soup or pasta pot over medium heat, cook chicken in water until tender, 45 minute to 1 hour; drain, rinse, cool and debone.
In a saucepan, heat the chicken broth and boil potatoes, carrots, onions and celery until tender, 15 to 20 minutes; drain, reserving broth.
Preheat oven to 400°F. Grease a 13x9x2-inch baking dish; set aside.
In a skillet, melt butter. Add flour, stirring until smooth. Cook for 1 minute, stirring constantly. Gradually stir in reserved broth, half-and-half, salt and pepper. Cook over medium heat, stirring occasionally, until thickened and bubbly.
Add the vegetables and chicken, stirring to coat, and pour into prepared 13x9x2-inch baking dish. Roll out the pie crusts and place on top, overlapping slightly in the center. Bake 30 to 35 minutes or until golden brown.