1. In a large pot, cook the chicken and sausage over medium heat until browned. Remove and set aside.
2. In the same pot, sauté the onion, bell pepper, celery, and garlic until tender.
3. Stir in the rice, chicken broth, diced tomatoes, Cajun seasoning, thyme, and bay leaves. Bring to a boil.
4. Reduce heat, cover, and simmer for 20 minutes.
5. Add the cooked chicken, sausage, and shrimp. Cook until the shrimp is pink and cooked through, about 5-7 minutes.
6. Remove bay leaves and serve hot.