In a large saucepan, bring chicken, water, salt and pepper to a boil. Reduce heat, cover and cook for about 20 minutes or until chicken is no longer pink.
Remove chicken from cooking liquid and cut into cubes. Set aside.
Add celery, onion, potato and carrot to cooking liquid. Bring to a boil. Reduce head and simmer for 10 minutes, or until vegetables are tender.
Add corn, milk and reserved chicken and reheat to serving temperature.