It was proposed that the id x 2 −y 2 density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small dxy component to the DDW state breaks the symmetry between the counter-propagating orbital currents of the DDW state and, thus, violates the macroscopic time-reversal symmetry. This symmetry breaking results in a non-zero polar Kerr effect, which has recently been observed in the pseudogap phase. 74.25.Nf, 71.27.+a Introduction. The nature of the pseudogap in the cuprate high-temperature superconductors is a much-debated and still unresolved issue [1]. Many of the anomalous properties associated with the pseudogap can be best described as resulting from the order parameters [2], such as those of various density-wave states, competing with the d-wave superconductivity. If a density-wave state were to have an energy gap of the d-wave symmetry on the Fermi surface, in conformity with the pseudogap, the natural candidate would be the id x 2 −y 2 density wave (DDW) state. Indeed, much of the phenomenology of the cuprates in the underdoped regime can be unified [3,4,5] by making a single assumption that the ordered DDW state is responsible for the pseudogap. However, the situation is still controversial, because there is no convincing direct experimental evidence for a phase transition to another state in the underdoped regime, besides the antiferromagnetic order close to half-filling.