Heat the oil in a large pan or pot to medium heat. Add the andouille sausage and cook 2-3 minutes to brown each side. Set aside into a bowl.
Add the chopped chicken and cook 2-3 minutes to brown each side. Set aside into a bowl with the smoked sausage.
To the pot, add onions, peppers and celery. Cook for 6-7 minutes, until softened.
Add garlic and cook 1 minute, until the garlic blooms and becomes fragrant.
Add Cajun seasonings, thyme, oregano, salt and pepper. Stir and cook 30 seconds to bloom the spices.
Add the rice and stir to coat. Cook 2-3 minutes to marry the flavors.
Add the chicken broth and reserved sausage and chicken. Top with bay leaves. Bring to a boil then reduce heat. Cover and simmer for 25-30 minutes, or until the rice is cooked and tender, to your preference. NOTE: If the rice is too wet, simmer with the lid off a few minutes to reduce excess liquid. Remove bay leaves.
Fluff with a fork, then garnish with chopped green onion and parsley. Serve with hot sauce on the side.
