Ubiquitin chains linked via lysine 48 (K48) of ubiquitin mediate recognition of ubiquitinated proteins by the proteasome. However, the mechanisms underlying polymerization of this targeting signal on a substrate are unknown. Here we dissect this process using the cyclin-dependent kinase inhibitor Sic1 and its ubiquitination by the cullin-RING ubiquitin ligase SCF(Cdc4) and the ubiquitin-conjugating enzyme Cdc34. We show that Sic1 ubiquitination can be separated into two steps: attachment of the first ubiquitin, which is rate limiting, followed by rapid elongation of a K48-linked ubiquitin chain. Mutation of an acidic loop conserved among Cdc34 orthologs has no effect on attachment of the first ubiquitin onto Sic1 but compromises the processivity and linkage specificity of ubiquitin-chain synthesis. We propose that the acidic loop favorably positions K48 of a substrate-linked ubiquitin to attack SCF bound Cdc34 approximately ubiquitin thioester and thereby enables processive synthesis of K48-linked ubiquitin chains by SCF-Cdc34.