Lightly grease the slow cooker or add olive oil to the base.
Place carrots, potatoes, celery, onion, and garlic into the slow cooker.
Lay the chicken on top of the vegetables and season with salt, pepper, thyme, and parsley.
Pour chicken broth over everything, ensuring the ingredients are mostly covered.
Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours, until the chicken is tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
For a thicker stew, mix cornstarch with water, stir it into the stew, and cook for an additional 15 minutes on HIGH.
Taste and adjust seasoning before serving.