Place the chicken breasts or thighs in the slow cooker.
Add chicken broth, fire-roasted diced tomatoes, black beans, diced onion, minced garlic, cumin, chili powder, and cayenne pepper. Stir to combine.
Cover and cook on low for 6-8 hours, or until the chicken is tender.
Remove the chicken from the slow cooker and shred it using two forks.
Return the shredded chicken to the slow cooker. Add lime juice and chopped cilantro. Stir well.
Taste and adjust seasoning with salt and black pepper as needed.
Serve hot with your favorite toppings, such as avocado, tortilla strips, or shredded cheese.