Chicken, Andouille, and Oyster Gumbo

Season the hen generously with salt and cayenne pepper.
Combine the oil and flour in a large, heavy pot or Dutch oven over medium heat. Stirring slowly and constantly, make a roux the color of chocolate. (When I attempted to make my first roux years ago, I remember calling Papa and asking him how long it would take, and he told me "the time it takes to drink two beers." Not being a beer drinker, I had to come up with my own system. I now put on two record albums, and when they have played out my roux is usually just about right.)
Add the onions, bell peppers, and celery, and cook, stirring, until they are soft, 10 to 12 minutes.
Add the chicken broth. (I usually warm it up in a pot just a bit before adding it to the roux mixture.) Stir to blend, and bring to a gentle boil.
Add the chicken. (There are those who will tell you to brown the chicken first, but I put it in raw.) Add the bay leaves and thyme, and cook at a gentle boil for 1 hour.
Add the andouille and cook, stirring occasionally, until the chicken is very tender, an hour to an hour and a half longer.
A few minutes before serving, add the oysters and simmer just until the oysters curl, about three minutes. Adjust seasoning to taste. (If the gumbo becomes too thick during cooking, simply add more chicken broth or water.)