We present results of first-principles density functional calculations for the candidate multiferroic magneto-electric, bismuth chromite. Although little is known experimentally about BiCrO3, its chemical neighbors BiMnO3 and BiFeO3 are known to be ferromagnetic and ferroelectric respectively, with structural distortions driven by the strongly polarizable Bi ions. Our calculations reveal, as expected, a Bi-induced distortion, and an octahedral Cr3+ ion which resists off-center displacement. We predict a G-type antiferromagnetic ground state, with an antiferrodistortive or antiferroelectric structural distortion, similar to that seen in PbZrO3.