In a stockpot, bring the chicken, water, onion, celery, carrot and 1/2 teaspoon salt to a boil. Reduce heat; cover and simmer for 50-60 minutes or until chicken is tender.
Remove chicken and vegetables from broth. Set aside until cool enough to handle. Meanwhile, line a 9-in. deep-dish pie plate with bottom pastry; trim even with edge of plate. Set aside.
Remove chicken from bones; discard skin and bones and cut chicken into cubes. Set aside. Chop the onion, celery and carrot. Strain broth and skim fat; set broth aside.
In a small bowl, combine the flour, onion salt, celery salt, pepper and remaining salt. Add 1/2 cup broth; whisk until smooth. In a large saucepan, bring 3 cups of broth to a boil; whisk in the flour mixture. Cook and stir for 2 minutes or until thickened. Remove from the heat; add chicken and vegetables. Pour into crust.
Roll out remaining pastry to fit top of pie; place over filling. Trim, seal and flute edges. Cut slits in top.
Cover edges loosely with foil. Bake at 400° for 40-45 minutes or until golden brown and filling is bubbly. Let stand for 15 minutes before cutting.