Place the chicken thighs in the bottom of the slow cooker.
Add the carrots, parsnips, turnip, onion, garlic, barley, chicken broth, thyme, bay leaves, salt, and pepper.
Stir everything together so the ingredients are evenly distributed.
Cover and cook on low for 7 hours or on high for 3½ hours, until the chicken is cooked through and the barley is tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Stir the stew, discard the bay leaves, and ladle into bowls.
Top each serving with chopped parsley.