Heat oil in a large pot over medium heat. Gradually whisk in flour, and cook, whisking constantly, until roux is a deep brown color, 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 browned, about 10 minutes.
Gradually stir in chicken broth. Bring to a boil, reduce heat to low, and simmer, uncovered, for 45 minutes.
Add okra, Cajun seasoning, salt, and pepper. Simmer for an additional 15 minutes.
Stir in green onions and parsley. Serve gumbo over cooked white rice.