Polyubiquitin chains linked through Lys48 are the principal signal for targeting substrates to the 26S proteasome. Through studies of structurally defined, polyubiquitylated model substrates, we show that tetraubiquitin is the minimum signal for efficient proteasomal targeting. The mechanism of targeting involves a simple increase in substrate affinity that is brought about by autonomous binding of the polyubiquitin chain. Assigning the proteasomal signaling function to a specific polymeric unit explains how a single ubiquitin can act as a functionally distinct signal, for example in endocytosis. The properties of the substrates studied here implicate substrate unfolding as a kinetically dominant step in the proteolysis of properly folded proteins, and suggest that extraproteasomal chaperones are required for efficient degradation of certain proteasome substrates.