Season the chicken with salt, pepper and Creole seasoning and brown quickly. Brown the sausage, pour off fat and reserve meats.
In a large, heavy pot, heat the oil and cook the flour in the oil over medium to high heat (depending on your roux-making skill), stirring constantly, until the roux reaches a dark reddish-brown color, almost the color of coffee or milk chocolate for a Cajun-style roux. If you want to save time, or prefer a more New Orleans-style roux, cook it to a medium, peanut-butter color, over lower heat if you're nervous about burning it.
Add the vegetables and stir quickly. This cooks the vegetables and also stops the roux from cooking further. Continue to cook, stirring constantly, for about 4 minutes.
Add the stock, seasonings, chicken and sausage. Bring to a boil, then cook for about one hour, skimming fat off the top as needed.
Add shelled and deveined shrimp, the chopped scallion tops and parsley, and heat for 5 minutes. Serve over rice in large shallow bowls.
Accompany with lots of hot, crispy French bread or serve in bread bowls.
Make sure to have plenty of Tabasco sauce on hand to give it a kick.