Sprinkle chicken with Creole seasoning. Heat oil in a Dutch oven over medium-high heat, add sausage and brown 2 minutes. Remove to a plate.
Add chicken and sauté until brown, about 4 minutes, remove to plate.
Add onions, celery, peppers, thyme, flour, and cayenne to pot and cook, stirring constantly, until onions are translucent, about 4 minutes.
Stir in rice, then add broth and tomatoes and bring to a boil. Reduce heat to low, cover and simmer 10 minutes.
Stir chicken and sausage into rice mixture, cover and continue to simmer 6 minutes. Stir in shrimp, cover and simmer 6 minutes, or until cooked through.
Spoon jambalaya into bowls and serve with warm corn bread.