Jets of highly energized plasma with relativistic velocities are associated with black holes ranging in mass from a few times that of the Sun to the billion-solar-mass black holes at the centres of galaxies. A popular but unconfirmed hypothesis to explain how the plasma is energized is the 'internal shock model', in which the relativistic flow is unsteady. Faster components in the jet catch up to and collide with slower ones, leading to internal shocks that accelerate particles and generate magnetic fields. This mechanism can explain the variable, high-energy emission from a diverse set of objects, with the best indirect evidence being the unseen fast relativistic flow inferred to energize slower components in X-ray binary jets. Mapping of the kinematic profiles in resolved jets has revealed precessing and helical patterns in X-ray binaries, apparent superluminal motions, and the ejection of knots (bright components) from standing shocks in the jets of active galaxies. Observations revealing the structure and evolution of an internal shock in action have, however, remained elusive, hindering measurement of the physical parameters and ultimate efficiency of the mechanism. Here we report observations of a collision between two knots in the jet of nearby radio galaxy 3C 264. A bright knot with an apparent speed of (7.0 ± 0.8)c, where c is the speed of light in a vacuum, is in the incipient stages of a collision with a slower-moving knot of speed (1.8 ± 0.5)c just downstream, resulting in brightening of both knots--as seen in the most recent epoch of imaging.