Fill a pot with water and bring to a boil. Cook the chicken breasts in the boiling water until no longer pink in the center and the juices run clear, about 10 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Drain and set aside to cool. Once cool, shred the chicken into small strands.
Fill the pot again with water and bring to a boil. Cook the tomatillos, jalapeno peppers, and nopales in the boiling water until the vegetables are all tender, about 5 minutes. Drain.
Blend the tomatillos and jalapeno peppers in a blender until smooth; pour into the pot with the shredded chicken and place over medium heat. Cut the nopales into small dice and add to the mixture. Allow the mixture to simmer until completely reheated, about 5 minutes.