A multisubunit complex called cohesin forms a huge ring structure that mediates sister chromatid cohesion, possibly by entrapping sister DNAs following replication. Cohesin's kleisin subunit Scc1 completes the ring, connecting the ABC-like ATPase heads of a V-shaped Smc1/3 heterodimer. Proteolytic cleavage of Scc1 by separase triggers sister chromatid disjunction, presumably by breaking the Scc1 bridge. One half of the SMC-kleisin bridge is revealed here by a crystal structure of Smc1's ATPase complexed with Scc1's C-terminal domain. The latter forms a winged helix that binds a pair of beta strands in Smc1's ATPase head. Mutation of conserved residues within the contact interface destroys Scc1's interaction with Smc1/3 heterodimers and eliminates cohesin function. Interaction of Scc1's N terminus with Smc3 depends on prior C terminus connection with Smc1. There is little or no turnover of Smc1-Scc1 interactions within cohesin complexes in vivo because expression of noncleavable Scc1 after DNA replication does not hinder anaphase.