Place the chicken breasts in the slow cooker. Add the chicken broth, minced garlic, lemon zest, lemon juice, oregano, salt, and black pepper.
Cover and cook on low for 6 hours until the chicken is tender and easy to shred.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the broth.
Add the fresh spinach to the slow cooker. Stir gently, cover, and cook for 10 more minutes until the spinach wilts.