Cook the chicken breasts in boiling water until no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove chicken from water and shred.
Mix cream of chicken soup, sour cream, and cheese cubes in a microwave-safe glass or ceramic bowl. Heat in the microwave in 3 minute intervals, stirring after each intervals, until the cheese is melted and the mixture has a smooth consistency. Add shredded chicken breast to chicken soup mixture and microwave for 2 minutes.
Pour corn chips into a large shallow bowl or serving dish. Pour hot chicken mixture over chips.
