Multiferroic BiCrO3 epitaxial films were grown by pulsed laser deposition on SrTiO3 (001) substrates with SrRuO3 bottom electrodes. The authors found that the films exhibit antiferroelectricity with a characteristic electric field induced ferroelectric phase, as evidenced by double hysteretic behaviors in the electric field dependence of dielectric constants and polarization. The antiferroelectricity is consistent with theoretical predictions that the Bi lone pair induces polarization in bismuth-based perovskites, such as ferroelectric BiMnO3 and BiFeO3. Magnetic measurements revealed weak parasitic ferromagnetism resulting from antiferromagnetic ordering below 140K. This magnetic transition coincides with a local maximum in the dielectric constants’ temperature dependence.