Chiral properties of the two phases - collinear motif (below Morin transition temperature, TM=250 K) and canted motif (above TM) - of magnetically ordered hematite ({alpha}-Fe2O3) have been identified in single crystal resonant x-ray Bragg diffraction, using circular polarized incident x-rays tuned near the iron K-edge. Magneto-electric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time-odd. Orbital angular momentum accompanies the collinear motif, while it is conspicuously absent with the canted motif. Intensities have been successfully confronted with analytic expressions derived from an atomic model fully compliant with chemical and magnetic structures. Values of Fe atomic multipoles previously derived from independent experimental data, are shown to be completely trustworthy.