When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-T c superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T * higher than T c , while phase coherence, and superconductivity, are established at T c (Refs. 1, 2). One would then wish to understand if T * is just a crossover, controlled by fluctuations in order which will set in at the lower T c (Refs. 3, 4), or whether some symmetry is spontaneously broken at T * (Refs. 5-10). Here, using angle-resolved photoemission with circularly polarized light, we find that, in the pseudogap state, left-circularly polarized photons give a different photocurrent than right-circularly polarized 2 photons, and therefore the state below T * is rather unusual, in that it breaks time reversal symmetry 11 . This observation of a phase transition at T* provides the answer to a major mystery of the phase diagram of the cuprates. The appearance of the anomalies below T* must be related to the order parameter that sets in at this characteristic temperature .We have investigated the time reversal invariance of the electronic states by ARPES, which becomes sensitive to this symmetry by the use of circularly polarized photons 11 .The measured ARPES intensity I α ∝ |M α | 2 , where the matrix element M α = 〈p|O α |ψ(k)〉, describes the ejection of the electron from an initial state |ψ(k)〉 to a final state |p〉, and the dipole operator O α contains the vector potential of α = L (left) or α = R (right) circularly polarized photons. The experimental setup is shown in Fig. 1. It consists of a plane grating monochromator beamline at the Aladdin synchrotron as a source of linearly polarized photons, quadruple reflection polarizer 12 , refocusing mirror, and the experimental chamber.It is crucial in this experiment, which is essentially measuring absolute intensity changes, to minimize beam movement, as extraneous intensity changes can occur from such movements.We therefore monitor the beam position, as shown in Fig. 1, finding a small residual beam movement of 150 µm, which is compensated for by adjusting the experimental chamber position as the polarizer is rotated. In the experiment one wishes to maximize the product TP 2 , where T denotes the transmission and P the polarization. In our experiment, this is accomplished with P = 86%, as shown in Fig. 1d. Although case (b) is the one that interests us, we first describe case (a), as this is a large effect, and needs to be correctly accounted for in the analysis of the data 13-15 . In Fig. 2a we it was found experimentally 16 , and confirmed here, that it is a symmetry direction for the CuO 2 planar electronic states). This is seen in Fig. 2e, where we plot spectra obtained at point M 1 that i...