Add the diced onion, celery, bell pepper, and garlic and stir well to coat the vegetables in the roux. Cook for 5 minutes or so to soften the vegetables, then add the andouille. Season the chicken with 1 tsp of the Cajun seasoning and add the chicken to the pot as well. Add the broth, oregano, thyme, bay leaves, and remaining Cajun seasoning and bring to a gentle simmer. Continue to cook for 45 minutes to an hour, during which time the gumbo will thicken and deepen for flavor. Simmer for longer if you have the time! The vegetables will disappear into the sauce, which should be velvety and delicious. Ladle over cooked white rice and garnish with green onions, if desired.