Combine the water and chicken in a Dutch oven, and bring to a boil. Reduce heat, and simmer 15 minutes or until chicken is done. Remove chicken from pan with a slotted spoon, reserving liquid. Remove chicken from bones; shred with 2 forks to measure 2 1/2 cups meat. Discard bones.
Add chicken, onion, and next 7 ingredients (onion through broth) to pan; bring to a boil. Reduce heat, and simmer 20 minutes or until vegetables are tender. Stir in noodles; cook over medium heat until thoroughly heated.