USP14 is a major regulator of the proteasome and one of three proteasome-associated deubiquitinating enzymes. Its effects on protein turnover are substrate-specific, for unknown reasons. We report that USP14 shows a marked preference for ubiquitin-cyclin B conjugates that carry more than one ubiquitin modification or chain. This specificity is conserved from yeast to humans and is independent of chain linkage type. USP14 has been thought to cleave single ubiquitin groups from the distal tip of a chain, but we find that it removes chains from cyclin B en bloc, proceeding until a single chain remains. The suppression of degradation by USP14's catalytic activity reflects its capacity to act on a millisecond time scale, before the proteasome can initiate degradation of the substrate. In addition, single-molecule studies showed that the dwell time of ubiquitin conjugates at the proteasome was reduced by USP14-dependent deubiquitination. In summary, the specificity of the proteasome can be regulated by rapid ubiquitin chain removal, which resolves substrates based on a novel aspect of ubiquitin conjugate architecture.