1. Heat the oil in a large pot over medium heat. Gradually whisk in the flour to make a roux. Cook, stirring constantly, until the roux is a dark brown color, about 15-20 minutes.
2. Add the chopped onion, bell pepper, and celery to the roux. Cook, stirring often, until the vegetables are tender, about 10 minutes.
3. Stir in the garlic and cook for another minute.
4. Gradually whisk in the chicken broth. Add the Cajun seasoning, thyme, and bay leaves. Bring to a simmer.
5. Add the chicken and sausage to the pot. Simmer uncovered for 45 minutes, stirring occasionally.
6. Add the okra and cook for another 15 minutes. Season with salt and pepper to taste.
7. Serve the gumbo over cooked white rice.