Place the chicken breasts in the slow cooker. Add the diced onion, sliced carrots, and minced garlic on top.
Pour in the chicken broth. Add the lemon zest, oregano, salt, and black pepper. Stir gently to combine the seasonings.
Cover and cook on low for 6 hours or until the chicken is tender and shreds easily.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Stir in the orzo and lemon juice. Cover and cook on high for 20 minutes until the orzo is tender.
Turn off the heat and stir in the fresh spinach until it wilts. Serve hot with crumbled feta on top.