Season chicken thighs with creole seasoning. Add to a large pot with oil, sear for about 7 minutes on both sides on medium heat, then set aside. Shred and cut chicken into smaller pieces.
In the same pot, add sausage, and sear for about 5 minutes on both sides, then set aside, keeping the excess fat in the pot.
Add oil and flour to the pot to make a roux on low to medium heat. Stir constantly for about 30 minutes until it is a chocolate brown color. Do not step away here because it can quickly burn.
Add onions, bell pepper, celery, and garlic. Cook until softened.
Add chicken broth, chicken, sausage, creole seasoning, and bay leaves. Simmer for at least an hour. Add shrimp during the last 5 minutes so it doesn't overcook.
Taste test and adjust to preference.
Serve with rice, green onions, and parsley. Hot sauce optional.