Add chicken broth, carrot, celery, zucchini, onion, oregano, garlic, and barley to a crockpot. Stir well.
Place chicken breasts into the crockpot.
Cover and cook on low for 4-6 hours, or until the chicken is cooked through and the barley is soft and chewy.
Remove chicken to a plate and shred with two forks.
Return shredded chicken to the crockpot.
Stir in the milk, Parmesan cheese, and pesto.
Turn the heat up to high and cook for another 10 minutes.
Ladle the soup into bowls and garnish with additional Parmesan cheese and/or pesto, as desired.