In a small pot, combine the chicken, water, onion, garlic, and salt. Bring to a boil then lower the heat to a low simmer and cook for two hours. Remove the chicken from the pot and strain the remaining vegetables in the broth. Place the strained broth into a clean pot; discard the onion and garlic.
Add the celery and carrots to the broth and bring to a simmer. Drop the gnocchi into the simmering broth a few at a time. While the gnocchi are cooking pull the meat from the chicken. Dice the chicken and add it to the simmering soup. Stir in the chopped parsley and serve while hot.