Dark matter particles gravitationally bound to our galaxy should exhibit a characteristic speed distribution limited by their escape velocity at the position of the Earth (vesc 550 km/s). An ongoing search for anomalous cosmic rays at Earth, kinematically similar to cold dark matter, is described. The technique can discriminate between these and known slow-moving particles such as neutrons, would be sensitive to telltale signatures from presently unexplored candidates, and offers the possibility of identifying the mediating type of interaction (nuclear vs. electron recoils). Studies of background identification and abatement in a shallow underground site are presented. The expected reach of the method is discussed, and illustrated by obtaining the first limits for dark matter particles lighter than 100 MeV/c 2 interacting via nuclear recoils. PACS numbers: 95.35.+d, 96.50.Zc, 29.40.Mc