Melt butter in a large Dutch oven; add chicken and ham. Cover and cook over medium heat 10 minutes, turning to brown all sides. Add onion, pepper, Creole seasoning, salt, and garlic salt; cook 5 minutes, stirring constantly. Add water.
Drain oysters, reserving oyster liquor; set oysters aside. Stir liquor into chicken mixture; bring to a boil. Reduce heat; cover and simmer 1 1/2 hours or until chicken is tender.
Remove chicken from broth, and cool. Bone chicken, and chop meat into bite-size pieces; discard bones. Return meat to broth. Bring to a boil. Stir in reserved oysters, and cook 3 minutes or until oyster edges begin to curl.
Stir in filé powder to taste just before serving. Serve gumbo over rice in individual bowls.