We investigate the chiro-optical properties of the electromagnetic near-field associated with the excitation of collective optical resonances (surface lattice resonances) in achiral plasmonic lattices. These arrays are specially designed to support dispersive resonances with nontrivial, multipolar near-field distributions in the surroundings of the nanostructure, which gives rise to an enhanced chiro-optical response. The presence of these multipolar resonances in lattices without explicitly broken mirror symmetry is experimentally confirmed by far-field extinction measurements, while the angular, spectral, and spatial dependence of the associated chiral near-field are numerically simulated. In contrast with typical pseudochiral systems, the extended chiro-optical near-field response appears even at normal incidence. We believe that surface lattice resonances in achiral plasmonic lattices can be potentially utilized as a substrate for enhanced background-free enantioselectivity and tunable chiral molecule recognition over large areas.