Combine water and chicken in large pot. Bring to boil. Reduce heat and simmer until chicken is tender, about 1 hour. Using tongs, transfer chicken to strainer and cool, saving cooking liquid. Remove meat from bones in pieces.
Heat 2 tablespoons oil in heavy skillet over medium heat. Add okra and cook until no longer sticky, stirring frequently, about 20 minutes; set aside.
Stir flour and remaining 1/2 cup oil in heavy large Dutch oven. Cook over medium heat until deep golden brown, stirring frequently, about 6 minutes. Add 4 cups reserved chicken cooking broth, okra, andouille sausage, tomatoes with their juices, bell pepper, celery, garlic, bay leaf, salt, thyme, basil, cayenne, and pepper. Cover partially and simmer until thickened, about 1 1/2 hours.
Spoon off any fat from surface of gumbo. Add chicken and file powder to gumbo and simmer gently 15 minutes. (If preparing ahead, cover and refrigerate. Bring to simmer before serving.) Mound rice in shallow bowls if desired. Ladle gumbo over and serve.
