We predict a new viscochiral regime of electronic transport in which spatially varying Hall viscosity selects vortical flow patterns. Although uniform Hall viscosity cannot alter incompressible bulk flow, its spatial gradient redistributes vorticity, amplifying vortices in one chamber while suppressing the vortex in the other. We further determine the underlying mechanism to be generic to recirculating flows and insensitive to the details of the device geometry. The paper maps the resulting phase diagram and shows that the regime is experimentally accessible in valley-polarized bilayer graphene.