Double pie pastry to line 10-inch deep-dish pan. In a large saucepan, cook chicken in broth for 30 minutes. Cool and reserve broth. In medium saucepan, add one cup reserved broth to onions, carrots, peas, and celery. Cook over medium heat 20 minutes. Remove from heat. In a small saucepan, cook butter and flour combination over low heat about one to two minutes. Slowly add remaining chicken broth and cook seven to ten minutes more, or until thickened. Preheat oven to 450°.
Remove chicken meat from bones and add to vegetable mixture, then blend in thickened stock. Season and pour into pastry-lined deep dish pan and cover with crust. Slit air vents for steam and bake ten minutes, then lower heat to 350° and continue baking 20 minutes until crust is golden brown.
