Heat oil in a large soup pot over medium heat. Add onions and garlic, and sauté until onion is soft, about five minutes. Add celery, carrots, zucchini, and parsnip, and cook an additional eight minutes.

Add water and barley. Bring to a boil, then simmer for 30 minutes. Add chicken breasts, salt, dill, and pepper. Let soup continue to simmer for one to one and a half hours.

Using a fork, shred the chicken breasts (you can do this in the pot or remove them for easier shredding).