We examine recent magnetic torque measurements in two compounds, γ-Li2IrO3 and RuCl3, which have been discussed as possible realizations of the Kitaev model. The analysis of the reported discontinuity in torque, as an external magnetic field is rotated across the c axis in both crystals, suggests that they have a translationally invariant chiral spin order of the form (Si·Sj×Sk)≠0 in the ground state and persisting over a very wide range of magnetic field and temperature. An extraordinary |B|B2 dependence of the torque for small fields, beside the usual B2 part, is predicted by the chiral spin order. Data for small fields are available for γ-Li2IrO3 and are found to be consistent with the prediction upon further analysis. Other experiments such as inelastic scattering and thermal Hall effect and several questions raised by the discovery of chiral spin order, including its topological consequences, are discussed. © 2018 American Physical Society.