Place the chicken bones or leftover chicken carcass in the slow cooker. Add the onion, carrots, celery, and garlic.
Pour in the apple cider vinegar and 8 to 10 cups of water, using enough water to mostly cover the bones and vegetables.
Add the salt and black pepper. Cover and cook on Low for 12 to 18 hours.
Carefully strain the chicken stock through a fine-mesh sieve into a large bowl or pot. Discard the bones, vegetables, and other solids.
Let the stock cool before transferring it to airtight containers. Refrigerate or freeze until ready to use.