Brown the sausage in a Dutch oven over medium heat. Remove and set aside on paper towels to drain.
Boil water in either an electric tea kettle or a separate pot on the stovetop. (see tip in the post above or notes below)
Add oil to a large pot and heat to medium. Add the onion, bell pepper, celery, and garlic. Saute until just tender, about 5 minutes.
Add half a jar of roux to the vegetables and stir together.
Gradually stir in boiling water to desired thickness. (see tip in the post above or notes below)
Add chicken, cajun seasoning, bay leaves, Worcestershire, and thyme according to the recipe and to your taste.
After the mixture heats on medium, turn it down to simmer uncovered for 45 minutes.
Add the sausage and green onions and cook for 15 more minutes.
Remove the bay leaves and serve over hot fluffy white rice.