Combine the oil and flour in a Dutch oven. Whisk the mixture over medium heat until well combined. Stir occasionally, until it turns into a slightly caramel color, about 10-15 minutes.
Add the onion, celery and pepper to the roux. Season with salt and pepper. Stir occasionally until softened, about 5-7 minutes. Add the broth, Worcestershire, bay leaf, chicken, andouille and canned tomatoes.
Reduce heat and simmer for 30 minutes, stirring occasionally. Season with hot sauce.