We propose a novel chiral order parameter to explain the unusual polar Kerr effect in underdoped cuprates. It is based on the loop-current model by Varma, which is characterized by the in-plane anapole moment N and exhibits the magnetoelectric effect. We propose a helical structure where the vector N (n) in the layer n is twisted by the angle π/2 relative to N (n−1) , thus breaking inversion symmetry. We show that coupling between magnetoelectric terms in the neighboring layers for this structure produces optical gyrotropy, which results in circular dichroism and the polar Kerr effect.PACS numbers: 74.72. Gh, 78.20.Jq, 78.20.Ek Introduction.-The nature of the pseudogap phase in underdoped cuprate superconductors has been a longstanding problem [1]. A series of optical measurements [2-5] revealed gyrotropy in this state. It was observed that the polarizations of incident and reflected light differ by a small angle θ K , called the polar Kerr angle. Initially, these experiments were interpreted as the evidence for spontaneous time-reversal symmetry breaking. Theoretical models [6-9] derived optical gyrotropy from the anomalous Hall effect. In these scenarios, the order parameter is equivalent to an intrinsic magnetic field perpendicular to the layers, which permeates the system and points inward and outward at the opposite surfaces of a crystal. Therefore, the Kerr angle should have opposite signs at the opposite surfaces of the crystal.However, recent reports [10,11] found that the Kerr angle has the same sign at the opposite surfaces of a sample. Therefore, the observed gyrotropy is not consistent with the time-reversal-symmetry breaking due to a magnetic order and should be interpreted as the evidence for natural optical activity due to chiral symmetry breaking [12]. Systems with helical structures, such as cholesteric liquid crystals and some organic molecules, typically exhibit optical gyrotropy and the polar Kerr effect. It is important that the sign of the Kerr angle in this case is the same at the opposite surfaces of the system, in contrast to the gyrotropy produced by a magnetic order (see