Heat a stock pot over medium heat and add oil. Add the sausage and cook for 2-4 minutes or until sides of sausage have browned. Add celery, onion, pepper, and garlic and cook for 6 minutes, stirring frequently.
Add rice and next 6 ingredients (through tomatoeand bring to a boil. Once boiling, cover, reduce heat, and simmer for 25-30 minutes or until rice is done.
Remove thyme and discard sprigs. Add the shredded chicken and stir until heated through, cooking about 3-5 minutes.
Serve warm and with crusty bread if desired.