Biogenesis of the eukaryotic 20S proteasome core particle (PC) is a complex process assisted by specific chaperones absent from the active complex. The first identified chaperone, Ump1, was found in a precursor complex (PC) called 15S PC. Yeast cells lacking Ump1 display strong defects in the autocatalytic processing of β subunits, and consequently have lower proteolytic activity. Here, we dissect an important interaction of Ump1 with the β7 subunit that is critical for proteasome biogenesis. Functional domains of Ump1 and the interacting proteasome subunit β7 were mapped, and the functional consequences of their deletion or mutation were analyzed. Cells in which the first sixteen Ump1 residues were deleted display growth phenotypes similar to ump1∆, but massively accumulate 15S PC and distinct proteasome intermediate complexes containing the truncated protein. The viability of these cells depends on the transcription factor Rpn4. Remarkably, β7 subunit overexpression re-established viability in the absence of Rpn4. We show that an N-terminal domain of Ump1 and the propeptide of β7 promote direct interaction of the two polypeptides in vitro. This interaction is of critical importance for the recruitment of β7 precursor during proteasome assembly, a step that drives dimerization of 15S PCs and the formation of 20S CPs.