Dedicated chaperones facilitate the assembly of the eukaryotic proteasome, but how they function remains largely unknown. Here we show that a yeast 20S proteasome assembly factor, Pba1-Pba2, requires a previously overlooked C-terminal hydrophobic-tyrosine-X (HbYX) motif for function. HbYX motifs in proteasome activators open the 20S proteasome entry pore, but Pba1-Pba2 instead binds inactive proteasomal precursors. We discovered an archaeal ortholog of this factor, here named PbaA, that also binds preferentially to proteasomal precursors in a HbYX motif-dependent fashion using the same proteasomal α-ring surface pockets as are bound by activators. PbaA and the related PbaB protein can be induced to bind mature 20S proteasomes if the active sites in the central chamber are occupied by inhibitors. Our data are consistent with an allosteric mechanism in which the maturation of the proteasome active sites determines the binding of assembly chaperones, potentially shielding assembly intermediates or misassembled complexes from nonproductive associations until assembly is complete.