Combine all the ingredients except the cilantro, pasta, and the lime juice into a slow cooker. Cover and cook on low about 8 hours. Remove the chicken from the soup and let it cool. When cool enough to handle, remove the meat from the bone and shred it back into the soup. Turn the temperature to high and add the broken angle hair pasta and stir in the lime juice. Finish cooking for about 30 minutes or until the pasta is tender.
Serve in bowls topped with the fresh cilantro and lime wedges.
Chicken - bone in chicken pieces are best for slow cooker soups. Chicken legs and thighs are flavorful and economical.