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. Save 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. Stir frequently for about 6 minutes. Add 4 cups reserved chicken cooking broth, okra, andouille sausage, tomatoes, bell pepper, celery, garlic, bay leaf, salt, thyme, basil, cayenne, and pepper. Cover partially and simmer until thickened (about 90 minutes).
Spoon off any fat from surface of gumbo. Add chicken and file powder to gumbo and simmer gently for 15 minutes. Mound rice in shallow bowls and ladle gumbo over rice, then serve.