Escherichia coli topoisomerase (Topo) IV is an essential type II Topo that removes DNA entanglements created during DNA replication. Topo IV relaxes (+) supercoils much faster than (-) supercoils, promoting replication while sparing the essential (-) supercoils. Here, we investigate the mechanism underlying this chiral preference. Using DNA binding assays and a single-molecule DNA braiding system, we show that Topo IV recognizes the chiral crossings imposed by the left-handed superhelix of a (+) supercoiled DNA, rather than global topology, twist deformation, or local writhe. Monte Carlo simulations of braid, supercoil, and catenane configurations demonstrate how a preference for a single-crossing geometry during strand passage can allow Topo IV to perform its physiological functions. Single-enzyme braid relaxation experiments also provide a direct measure of the processivity of the enzyme and offer insight into its mechanochemical cycle.