The question posed was "what is the punishment for students caught chesting?" It is entirely possible that there is a college campus craze referred to as "chesting," but for purposes of discussion, it will be assumed that a typo was involved and the word "cheating" was intended.
Almost every academic institution of higher learning has a written code of conduct to which every student is supposed to be held. Those codes of conduct state explicitly what are the penalties for cheating. Most such institutions have experienced problems with cheating at one time or another, including some of the most prestigious universities in the country. As recently as February 2013, Harvard expelled as many as 70 students suspected of cheating on a take-home exam. Similarly, the nation's service academies have expelled midshipmen and cadets for cheating.
Expulsion is the most common penalty imposed for cheating. Depending upon the circumstances, students might "only" be suspended for a semester or a year, but expulsions are routine in such matters.