A theory for the phenomena observed in Copper-Oxide based high temperature
superconducting materials derives an elusive time-reversal and rotational
symmetry breaking order parameter for the observed pseudogap phase ending at a
quantum-critical point near the composition for the highest Tc. An
experiment is proposed to observe such a symmetry breaking. It is shown that
Angle-resolved Photoemission yields a current density which is different for
left and right circularly polarized photons. The magnitude of the effect and
its momentum dependence is estimated. Barring the presence of domains of the
predicted phase an asymmetry of about 0.1 is predicted at low temperatures in
moderately underdoped samples.Comment: latex, 2 figure