DNA gyrase is a molecular machine that uses the energy of ATP hydrolysis to introduce essential negative supercoils into DNA. The directionality of supercoiling is ensured by chiral wrapping of the DNA around a specialized domain of the enzyme before strand passage. Here we observe the activity of gyrase in real time by tracking the rotation of a submicrometre bead attached to the side of a stretched DNA molecule. In the presence of gyrase and ATP, we observe bursts of rotation corresponding to the processive, stepwise introduction of negative supercoils in strict multiples of two. Changes in DNA tension have no detectable effect on supercoiling velocity, but the enzyme becomes markedly less processive as tension is increased over a range of only a few tenths of piconewtons. This behaviour is quantitatively explained by a simple mechanochemical model in which processivity depends on a kinetic competition between dissociation and rapid, tension-sensitive DNA wrapping. In a high-resolution variant of our assay, we directly detect rotational pauses corresponding to two kinetic substeps: an ATP-independent step at the end of the reaction cycle, and an ATP-binding step in the middle of the cycle, subsequent to DNA wrapping.