Heat 1 tablespoon of olive oil in a large pot over medium heat.
Add the sliced sausage and brown it for about 5 minutes or until it is crispy.
Remove it from the pot and set aside.
In the same pot, add the cubed chicken and cook for 6-8 minutes until lightly browned on all sides.
Remove the chicken and keep it with the sausage.
Add the remaining olive oil to the pot.
Add the chopped onion, bell pepper, celery, and garlic, cooking over medium heat for about 5 minutes until the vegetables are tender.
Add rice to the pot with the vegetables and stir for 2 minutes.
Stir in the chicken broth, diced tomatoes, cajun seasoning, salt, black pepper, paprika, thyme, and bay leaves.
Return the sausage and chicken to the pot.
Bring the mixture to a simmer and then cover.
Lower the heat, cook for 20-25 minutes, or until the rice is tender.
Near the end of cooking, add the shrimp to the pot.
Cover and cook for an additional 5 minutes or until the shrimp is pink and cooked through.
Remove bay leaves, garnish with green onions, and serve hot.