Add the chicken breasts to the slow cooker along with the broth, carrots, celery, onion, garlic, oregano, salt, and pepper.
Cover and cook on low for 6 hours until the chicken is fully cooked and tender.
Remove the chicken from the pot, shred it with two forks, and return the pieces to the broth.
Stir in the orzo along with the lemon juice and lemon zest.
Cover and cook on high for 20 to 30 minutes until the orzo is tender.
Ladle into bowls and top each serving with fresh parsley.