Heat oil in a large pot over medium heat. Gradually whisk in flour, and cook, whisking constantly, until roux is chocolate brown, about 20-30 minutes.
Add onion, bell pepper, celery, and garlic. Cook, stirring often, until vegetables are tender, about 10 minutes.
Stir in sausage and chicken, and cook until chicken is browned, about 5 minutes.
Gradually stir in chicken stock. Add okra, Creole seasoning, thyme, and bay leaves. Bring to a boil, reduce heat, and simmer for 45 minutes.
Add shrimp and cook until pink, about 5 minutes. Season with salt and pepper to taste. Serve over cooked white rice.