In a large pot or Dutch oven, cook the chicken and sausage over medium heat until browned. Remove and set aside.
Add the onion, celery, and bell pepper to the pot and sauté until softened.
Stir in the minced garlic and cook for an additional minute.
Return the chicken and sausage to the pot, along with the crushed tomatoes, chicken stock, rice, and optional ingredients if desired.
Season with Cajun seasoning, thyme, and cayenne pepper.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for about 20 minutes or until the rice is cooked and the flavors have melded together.
During the last 5 minutes of cooking, add the peeled and deveined shrimp.
Remove from heat and let stand for a few minutes before serving.