We report the observation of a highly unusual Hall current in the helical magnet MnSi in an applied pressure P=6-12 kbars. The Hall conductivity displays a distinctive stepwise field profile quite unlike any other Hall response observed in solids. We identify the origin of this Hall current with the effective real-space magnetic field due to chiral spin textures, which may be a precursor of the partial-order state at P>14.6 kbar. We discuss evidence favoring the chiral spin mechanism for the origin of the observed Hall anomaly.