Heat oil in a large pot or Dutch oven over medium heat
Add diced onion, bell pepper, and celery
Cook until softened
Add minced garlic and cook briefly
Add sliced sausage and cook until browned
Add chicken pieces and cook until lightly browned
Stir in Cajun seasoning, salt, black pepper, thyme, and bay leaves
Add diced tomatoes if using
Add rice and stir to coat
Pour in chicken broth
Bring to a boil
Reduce heat to low
Cover and simmer until rice is tender and liquid is absorbed
Stir in shrimp during the last few minutes if using
Remove from heat
Let rest covered for a few minutes
Fluff with a fork
Serve hot