In a large pot, heat the olive oil and butter over medium-high heat. Add the sausage and cook until browned on both sides, for about 5 minutes or so. Remove the sausage and set aside. Do not drain any grease from the pot.
To the same pot, add the chicken. Sprinkle the salt and pepper onto the chicken and add the minced garlic. Cook the chicken on medium-high heat until browned on all sides, about 3- 5 minutes. Remove the chicken from the pot and set aside.
Sauté the onions, bell pepper, and celery until they just begin to soften. Add in the creole seasoning, smoked paprika, thyme, crushed tomatoes, chicken stock, and bay leaves. Return the chicken and sausage to the pot and stir to combine. Bring to a boil.
Stir in the rice and reduce heat to low. Cover the pot with a lid and continue to cook for 20-25 minutes, until all the liquid is absorbed.
Remove the bay leaves from the pot and serve.