We report the first observation of a nonreciprocal x-ray linear dichroism caused by the time-reversal odd, real part zeta of the complex gyrotropy tensor zeta(*) which is dominated by electric dipole-electric quadrupole E1E2 interference terms. A nonreciprocal transverse anisotropy was observed in the low temperature insulating phase of a Cr doped V2O3 Mott crystal when a single antiferromagnetic domain was grown by magnetoelectric annealing along the hexagonal c axis. This new element (edge) specific spectroscopy could nicely complement x-ray magnetic circular dichroism which is silent for antiferromagnetic materials.