In a large pot, heat the vegetable oil over medium heat. Add the flour to make a roux, stirring constantly until it turns a dark brown color (be careful not to burn it).
Add the diced chicken and sausage to the pot, cooking until the chicken is browned.
Stir in the onion, bell pepper, celery, and garlic, cooking until the vegetables are softened.
Pour in the chicken broth and diced tomatoes. Add the bay leaves, Cajun seasoning, thyme, salt, and pepper.
Bring the gumbo to a boil, then reduce the heat and let it simmer for about 45 minutes to let the flavors meld together.
Serve the Cajun Chicken and Sausage Gumbo over cooked rice.
Enjoy!