Mix chicken broth, black beans, diced tomatoes, pale ale, corn, red enchilada sauce, onion, taco seasoning, and jalapeno pepper together in a slow cooker. Add whole chicken breasts.
Cook on Low until an instant-read thermometer inserted into the center of the chicken reads at least 165 degrees F (74 degrees C), 5 to 6 hours. Remove chicken and shred using 2 forks; stir back into the slow cooker. Continue cooking, 1 to 2 hours more.
Stir cilantro into the slow cooker. Cook on Low until flavors combine, about 15 minutes.