Recent reports that macroscopic vortex flows can discriminate between chiral molecules or their assemblies sparked considerable scientific interest both for their implications to separations technologies and for their relevance to the origins of biological homochirality. However, these earlier results are inconclusive due to questions arising from instrumental artifacts and/or insufficient experimental control. After a decade of controversy, the question remains unresolved-how do vortex flows interact with different stereoisomers? Here, we implement a model experimental system to show that chiral objects in a Taylor-Couette cell experience a chirality-specific lift force. This force is directed parallel to the shear plane in contrast to previous studies in which helices, bacteria and chiral cubes experience chirality-specific forces perpendicular to the shear plane. We present a quantitative hydrodynamic model that explains how chirality-specific motions arise in non-linear shear flows through the interplay between the shear-induced rotation of the particle and its orbital translation. The scaling laws derived here suggest that rotating flows can be used to achieve chiral separation at the micro- and nanoscales.