We report the first experimental detection of x-ray magnetochiral dichroism in magnetoelectric Cr2O3. This dichroism, which does not require any polarized x-ray beam, is related to the time-reversal odd part of the optical activity tensor dominated by electric dipole-electric quadrupole E1E2 interference terms. The experiments were carried out using either a single crystal or a powdered pellet required to grow a single antiferromagnetic domain by magnetoelectric annealing. This new element (edge) specific spectroscopy offers unique access to the atomic orbital anapole moment Omega-z.