Sprinkle salt and pepper over chicken pieces. Brown chicken and ham in butter in a large Dutch oven. Set aside.
Drain oysters; add water to oyster liquid to measure 2 quarts. Refrigerate oysters.
Combine oyster water and next 8 ingredients, stirring well; add to Dutch oven. Simmer 1 1/2 hours or until chicken is tender.
Remove chicken from broth; bone, and cut into bite-size pieces. Return chicken to broth. Cool; cover and refrigerate overnight.
Skim fat from cold gumbo, and bring to a boil; reduce heat, and add oysters. Heat thoroughly and serve over rice. Add a small amount of filé to each serving, if a thicker gumbo is desired.