Heat up a Dutch Oven over a medium-high flame. Pour in the peanut oil in. When the heat comes up slightly, sprinkle in the flour. Stir to combine with a wire whip. Watch and whisk the roux constantly until the roux becomes dark chocolate brown in color. This process should take 6-8 minutes.
Lower the flame. Carefully place the onions, bell pepper and celery into the roux. Add a little salt, and saute for 8 minutes. Break the roux down with wine and cold water. Add ground cayenne pepper and salt to taste.
Dry off the chicken pieces with paper towels. In a skillet, sear the chicken in peanut oil until both sides are golden-brown. Move the chicken to the Dutch oven. Brown the sausage, then move the sausage to the Dutch oven. Degease the skillet, then deglaze it with wine. Scrape the bottom of the skillet to release the brown-bits. Pour the wine reduction into the Dutch oven. Allow the liquids to reach a boil. Reduce the heat to a simmer, cover the pan with a tightly fitting lid and braise for 1 hour or so. Serve over rice or pasta.