In a 3-1/2- or 4-quart slow cooker, combine chicken, chile peppers, onion, oregano, garlic, and cayenne pepper. Pour enchilada sauce over chicken mixture, coating the chicken. Cover and cook on low-heat setting for 5 to 6 hours or on high-heat setting for 1-½ to 3 hours. Remove chicken from slow cooker, reserving cooking liquid. When chicken is cool enough to handle, use two forks to pull chicken apart into shreds. Place shredded chicken in a serving bowl. Stir in enough of the reserved cooking liquid to moisten. If desired, use the remaining cooking liquid to make Chile Enchilada Sauce.