A measurement of the low-velocity moderation of Σ- hyperons in hydrogen has been performed in a bubble-chamber experiment. The technique employed determines very accurately the Σ- velocity at decay, ∆β=+/-0.004, by using Σ--->π-+n decays accompanied by neutron scatters with visible proton recoils. The results of the study, based on 23 200 Σ- leading to 151 events with recoils in the region βΣ-<0.10, indicate that the Σ- moderation time for β>0.02 agrees with the predictions of energy-loss theory using the first-order Born approximation and with experimental energy-loss data for protons. However, for the region 0.01<β<0.02, the moderation-time data for Σ- (and π-) in hydrogen no longer agree with calculations based on the Born approximation or with experimental data for protons. The results for hydrogen are discussed and interpreted as being related to an "excess-range" effect previously observed for negative particles in emulsion.