We investigate the Hall response of hardcore bosonic atoms on a triangular ladder in a magnetic field. To access the dynamical properties of this many-body quantum system, we employ matrix product states numerical methods. We show that the behavior of the Hall polarization, both in its saturation value and in the short-time dynamics, correlates with the features of the underlying phase diagram, which stem from the interplay of interactions and geometric frustration. This paves the way to employ the Hall response as a sensitive probe of many-body chiral quantum phases in strongly correlated materials.