In a slow cooker, mix the chicken, sausage, tomatoes with juice, onion, garlic, celery, and broth. Season with oregano, parsley, Cajun seasoning, cayenne pepper, and thyme. (I do this the night before and put it in the fridge. I put it in the slow cooker before I leave in the morning.)
Cover, and cook 7 to 8 hours on Low, or 3 to 4 hours on High. Mix in cooked rice cook for about 15 minutes to warm through.
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