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.
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