Pulled chicken can become tough if it's overcooked, especially if you use white meat. If you're accustomed to making pulled pork, you'll know that long, slow cooking results in a tender shreds of pork; however, there's an important difference between pork and chicken breasts. Pork, especially pork shoulder which is commonly used for pulled pork, contains a lot of fat which keeps the meat moist and tender. In contrast, chicken breasts are very low in fat. To remedy this, remember that chicken doesn't have to cook as long as pork. Allow the shredded chicken to soak in the cooking liquid. If you have time, refrigerate the chicken in the liquid overnight to let it absorb the flavorful juices.