Place first 5 ingredients in a Dutch oven. Bring to a boil; cover, reduce heat, and simmer 20 minutes or until chicken is done. Transfer chicken to a cutting board, and remove chicken from bones, discarding skin and bones. Coarsely chop chicken.
Strain cooking liquid through a sieve over a bowl, discarding vegetables and solids. Return liquid to pan. Add onion and next 3 ingredients; bring to a boil. Cover, reduce heat, and simmer 13 minutes. Stir in chopped chicken, noodles, and remaining ingredients. Cover and simmer 10 minutes.