All organisms have evolved mechanisms to manage the stalling of ribosomes upon translation of aberrant mRNA. In eukaryotes, the large ribosomal subunit-associated quality control complex (RQC), composed of the listerin/Ltn1 E3 ubiquitin ligase and cofactors, mediates the ubiquitylation and extraction of ribosome-stalled nascent polypeptide chains for proteasomal degradation. How RQC recognizes stalled ribosomes and performs its functions has not been understood. Using single-particle cryoelectron microscopy, we have determined the structure of the RQC complex bound to stalled 60S ribosomal subunits. The structure establishes how Ltn1 associates with the large ribosomal subunit and properly positions its E3-catalytic RING domain to mediate nascent chain ubiquitylation. The structure also reveals that a distinguishing feature of stalled 60S particles is an exposed, nascent chain-conjugated tRNA, and that the Tae2 subunit of RQC, which facilitates Ltn1 binding, is responsible for selective recognition of stalled 60S subunits. RQC components are engaged in interactions across a large span of the 60S subunit surface, connecting the tRNA in the peptidyl transferase center to the distally located nascent chain tunnel exit. This work provides insights into a mechanism linking translation and protein degradation that targets defective proteins immediately after synthesis, while ignoring nascent chains in normally translating ribosomes.