Melt shortening in a large stockpot; stir in flour. Cook over medium heat, stirring occasionally, 10 minutes or until roux is the color of a copper penny. Add onion, celery, green pepper, and garlic; cook until vegetables are tender. Set aside.
Brown chicken in oil in a large skillet; drain, and set aside. Reserve drippings in skillet.
Add water to skillet, and bring to a boil. Remove from heat, and gradually pour pan dripping mixture over vegetable-flour mixture in stockpot, stirring constantly. Add chicken, sausage, salt, and pepper; cover and simmer 1 to 1 1/2 hours, stirring occasionally. Remove from heat; stir in filé powder. Serve gumbo over rice.