Combine chicken, onion, salt, pepper, and water in a large Dutch oven; bring to a boil. Reduce heat; cover and simmer 20 minutes.
Add carrots, parsnips, and celery; stir well. Place parsley on top of soup; cover and simmer an additional 3 hours.
Remove chicken and vegetables from soup; set aside. Discard parsley. Strain broth through several layers of damp cheesecloth. Remove chicken from bones, and coarsely chop; return chicken and vegetables to strained broth. Place over medium heat, and cook until thoroughly heated.
Ladle soup into individual serving bowls; serve warm.