Chop celery, onion, and bell pepper into small, 1/2 inch pieces. Slice the sausage into 1/2 inch moons or half moons. Mince the garlic.
Combine chicken, sausage, chopped veggies, diced tomatoes, and broth in the crock pot. Stir in oregano, thyme, creole spice, and cayenne.
Cover and cook on low 7-8 hours, or on high 3-4 hours. Turn the crock pot to high and let the liquid come to a boil. Remove chicken and shred it with a fork, then return to the pot along with the rice. Cover and let cook another 20-25 minutes on high.
Stir to fluff the rice and ensure most of the liquid has cooked out. Garnish and serve!
Wanna punch it up? Toss in a few jalapeños or serrano peppers.