Combine chicken, squash, stock, onion, garlic, bay leaf, salt, oregano, fennel seeds, and pepper in a 5- to 6-quart slow cooker. Cover and cook on low until chicken is very tender, about 6 hours.
Place chicken on a cutting board. Add quinoa to slow cooker. Cover and cook on low until quinoa is cooked, about 30 minutes. Shred chicken; stir into stew. Discard bay leaf.