In a slow cooker, combine chicken, sausage, tomatoes, onion, green pepper, celery, and chicken broth. Stir in oregano, Cajun seasoning, hot sauce, bay leaves, and thyme.
Cover, and cook on LOW for 7 hours or on HIGH for 3 hours. Stir in the thawed shrimp, cover and cook until the shrimp is heated through, about 5 minutes. Discard bay leaves and spoon mixture over cooked rice.