In a medium bowl, whisk together the fresh lime juice, chopped cilantro, minced garlic, ground cumin, chili powder, salt, and black pepper.

Place the chicken breasts in the basin of a 4 to 6-quart slow cooker. Pour the marinade mixture evenly over the chicken.

Cover the slow cooker and cook on LOW for 6 to 8 hours, or on HIGH for 3 to 4 hours, until the chicken is very tender and easily shreds.

Remove the chicken breasts from the slow cooker and place them on a large cutting board. Use two forks to shred the chicken thoroughly.

Return the shredded chicken to the slow cooker. Stir well to coat the chicken completely with the cooking liquid and juices. If the sauce seems too thin, stir in 1/4 cup of chicken broth for richness.

Cook on WARM (or cover and cook on HIGH for 15 minutes) for final flavor melding before serving. Taste and add more salt or lime juice if necessary.