Place the chicken breasts in the bottom of the slow cooker. Add the barley, carrots, celery, and onion on top.
Pour the chicken broth over the ingredients. Stir in the garlic, thyme, bay leaf, salt, and pepper.
Cover and cook on low for 7 hours until the chicken is cooked through and the barley is tender.
Remove the chicken from the slow cooker. Shred it with two forks, then return it to the pot.
Stir in the chopped spinach and let it sit for 5 minutes until wilted. Remove the bay leaf before serving.