Cohesin is a multisubunit complex that mediates sister-chromatid cohesion. Its Smc1 and Smc3 subunits possess ABC-like ATPases at one end of 50 nm long coiled coils. At the other ends are pseudosymmetrical hinge domains that interact to create V-shaped Smc1/Smc3 heterodimers. N- and C-terminal domains within cohesin's kleisin subunit Scc1 bind to Smc3 and Smc1 ATPase heads respectively, thereby creating a huge tripartite ring. It has been suggested that cohesin associates with chromosomes by trapping DNA within its ring. Opening of the ring due to cleavage of Scc1 by separase destroys sister-chromatid cohesion and triggers anaphase. We show that cohesin's hinges are not merely dimerization domains. They are essential for cohesin's association with chromosomes, which is blocked by artificially holding hinge domains together but not by preventing Scc1's dissociation from SMC ATPase heads. Our results suggest that entry of DNA into cohesin's ring requires transient dissociation of Smc1 and Smc3 hinge domains.