Just about any cut of chicken will work for this soup. It mostly comes down to the amount of work you are willing to do as far as skimming and separating the meat after cooking. The easiest choice is boneless, skinless chicken breast. Just shred once cooked and toss back into the soup. However, a cut with bones will add more flavor to the stock, such as bone-in breasts, thighs, or wings. Just keep in mind that these cuts are a little more work.