The Supreme Court has ruled on it three times. In 1962, they ruled that prayer can not be initiated by a public school, as that would violate the Establishment Clause. In 1992, they expanded on that ruling to say that schools can not invite members of the clergy (even non-denominational ones like they have at The Chapel across the street from campus) to lead prayer on school grounds. Finally in 2000, they ruled that students can engage in prayer that is voluntary, led by the students and done without official permission from the school, which means that school officials/employees can not make an announcement or acknowledge that a time for prayer is about to begin.
I don't have a problem with it, but when the Supreme Court rules three times on something, I figure that it's best to steer far, far away from that topic when you're a large and highly-visible government institution.