In a large saucepan bring the water to boiling. Add chicken breast. Return to boiling; reduce heat. Cover and simmer for 20 to 25 minutes or until chicken is tender and no loner pink. Remove chicken.
Add onion, carrot, and celery to cooking liquid. Return to boiling; reduce heat. Simmer, uncovered, for 10 minutes.
When cool enough to handle, remove chicken from bones; discard bones. Chop the chicken. Stir soup and milk into vegetable mixture until smooth. Add chicken and cubed cheese; heat and stir until cheese melts. If desired, garnish with shredded cheese.