In the base of your slow cooker, combine the onion, carrots, celery, garlic, thyme, parsley, bay leaves, white wine, broth, salt, and pepper; stir. Add the chicken breasts (make sure they’re covered with the liquid).
Cover and cook until chicken is tender, about 4 hours on low or 2-3 hours on high. Transfer the chicken to a cutting board and use 2 forks to shred chicken into bite-size pieces. Discard the thyme sprigs and and bay leaves.
Stir the instant rice into the soup in the slow cooker. Cover and cook until tender, 10-15 minutes. Return the shredded chicken to the soup. Add the parsley. Taste and season with more salt and pepper if desired. Serve.