We show that an atomic system in a periodically modulated optical trap displays an ideal mean-field symmetry-breaking transition. The symmetry is broken with respect to time translation by the modulation period. We describe experimental observations and develop a full microscopic theory of the observed critical phenomena. The transition is explained as resulting from the interplay of the long-range interatomic interaction and nonequilibrium fluctuations in the strongly modulated system. The observations, including anomalous fluctuations in the symmetry broken phase, are fully described by the theory.