Heat a large heavy pot on medium heat. Add the oil, carrots, onion, celery and garlic to the pot and stir.
Add chicken, broth, parsley, and bay leaf and bring to a boil. When boiling, reduce heat to low and cover. Simmer covered over low heat until the chicken and vegetables are tender, about 30 minutes.
Remove the chicken, shred, and return the chicken to the pot along with the barley, adjust the salt if needed and add fresh ground pepper. Simmer an additional 40 minutes, until the barley is cooked.
Discard bay leaf and serve.