  Polar Kerr effect in the high-Tc superconductor \YBCO was measured at zero
magnetic field with high precision using a cyogenic Sagnac fiber
interferometer. We observed non-zero Kerr rotations of order $\sim 1 \mu$rad
appearing near the pseudogap temperature $T^*$, and marking what appears to be
a true phase transition. Anomalous magnetic behavior in magnetic-field training
of the effect suggests that time reversal symmetry is already broken above room
temperature.
