Mix flour and salt. Cut in shortening, butter and cheese till crumbs form. Add water and toss with a fork just until dough just forms a ball.
Turn onto lightly floured board. Press large chunks away with heel of hand. Gather and repeat. Shape into thick circle. Wrap in plastic and chill at least 30 minutes.
Stew chicken with enough water to cover it, along with the onion and celery, until done. This usually takes from 60 to 90 minutes.
Remove chicken from broth. Debone and skin. Chop meat.
Skim off fat from broth. Discard the celery and onion. Reserve 3 cups broth for this recipe. (The more concentrated the broth, the better.).
Melt butter. Add flour. Cook and stir until bubbly. Add reserved broth and evaporated milk. Don't just dump all the liquids into the flour mixture--work in about 1/4 cup at a time until it is thinned out, and then you can increase how much liquid you can work in each time. Season with salt and pepper. Mix in chicken. Put chicken filling in a round casserole dish.
Roll out dough, a little bigger than your dish so that you can have some dough to crimp. Place dough over chicken filling. Crimp edges.
Bake at 425 degrees for about 30-60 minutes or until crust is golden. If you check it and the edges of the pie are looking browned before the rest of it is ready, put foil over the edges -- just make like a long little tent and loosely attach over the edges.