Meanwhile, we heat our dutch oven over medium high heat with 1 tablespoon of oil. We salt and pepper the chicken and when the oil is hot we add half the chicken. We brown for about 5 minutes, turning after 3 minutes. We remove the chicken to a plate and continue with the rest of the chicken. When all the chicken is browned, we set the pieces aside and remove as much skin as we can. We kept the skin to add flavor to the pan, but we do not need the skin on in the stew.
We add the rest of the vegetable oil and the butter to the dutch oven. We lower the heat to medium, and when the butter has melted, we add the flour. We stir with a wooden spoon, scraping up the brown bits on the bottom of the pan. We cook, stirring often, for about 10 minutes. We want the butter-flour mixture to be darkish brown. When it looks good, we add the onions. We stir and cook for about 5 minutes. Next we add the peppers and celery. After another 5 minutes, we add the garlic, dried thyme and rosemary, and the sausage. We stir and add the wine. When the wine is almost evaporated, we strain the chicken stock from the pot into the dutch oven and add the browned chicken. We bring the mixture to a boil, lower it to a gentle simmer, and partially cover the dutch oven.
After 30 minutes of simmering, we can taste the stew for seasoning. In a cup we mix the rest of the water with the Worcestershire sauce, cayenne powder, and salt and pepper. We then continue to simmer for another 45 minutes partially covered.
Meanwhile, we make the rice according to the package directions. We chop the tomato and salt it. When the chicken is very tender, we shut the heat on the dutch oven and add the tomato and half the chopped parsley. After about 5 minutes, we serve the chicken andouille stew over the cooked rice.
We top with the remaining parsley and hot pepper sauce if desired.