Place a large pot or Dutch oven over medium high heat and add the oil. Once the oil is hot add the sausage and cook for 2 minutes. Then add the chicken to the pot and cook for 6-8 minutes. Then remove the chicken and sausage from the pot.
Add the onions, peppers, and celery to the pot and cook for about 5 minutes, add the garlic part way through. Add the chicken and sausage, thyme, oregano, Cajun seasoning, bay leaves, Worcestershire sauce, broth and diced tomatoes. Stir to combine everything.
Bring it to a boil and turn it down to a simmer and add the rice and cook for 30-40 minutes or until the rice has absorbed all the liquid.
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