We propose that the enigmatic pseudogap phase of cuprate superconductors is
characterized by a hidden broken symmetry of d(x2-y2)-type. The transition
to this state is rounded by disorder, but in the limit that the disorder i
s made sufficiently small, the pseudogap crossover should reveal itself to
be such a transition. The ordered state breaks time-reversal, translational
, and rotational symmetries, but it is invariant under the combination of a
ny two. We discuss these ideas in the context of ten specific experimental
properties of the cuprates, and make several predictions, including the exi
stence of an as-yet undetected metal-metal transition under the superconduc
ting dome.