In a 5- to 6-quart slow cooker, place the chicken, carrots, celery, onion, garlic, bay leaves, 6 cups water, 1 teaspoon salt, and ¼ teaspoon pepper.
Cook, covered, until the chicken is cooked through, on high for 4 to 5 hours or on low for 7 to 8 hours (the low setting will make total cooking time 8 ½ hours).
Twenty minutes before serving, transfer the chicken to a bowl. Remove and discard the onion and bay leaves. If the slow cooker is on the low setting, turn it to high. Add the pasta to the slow cooker, cover, and cook until tender, 15 to 18 minutes.
Meanwhile, shred the chicken. When the pasta is cooked, stir the chicken into the soup along with the parsley. Serve with the crackers, if desired.