Bring first 8 ingredients to a boil in a large Dutch oven or stockpot over medium-high heat. Reduce heat to low, cover, and simmer 1 hour or until chicken is tender. Remove from heat, and let stand 15 minutes.
Remove and discard celery, carrots, and bay leaf from broth, reserving broth in Dutch oven. Remove chicken and cool slightly; remove skin and bones, and coarsely chop.
Sauté sausage in a large skillet over medium-high heat 5 minutes or until browned; drain.
Add chicken and sausage to reserved broth in Dutch oven, and bring to a boil over medium-high heat; stir in rice, and return to boil. Cover, reduce heat to low, and cook 20 minutes or until broth is absorbed and rice is tender.