The binary neutron-star merger GW170817(1) was accompanied by radiation across the electromagnetic spectrum(2) and localized(2) to the galaxy NGC 4993 at a distance(3) of about 41 megaparsecs from Earth. The radio and X-ray afterglows of GW170817 exhibited delayed onset(4-7), a gradual increase' in the emission with time (proportional to t(0.8)) to a peak about 150 days after the merger event(9), followed by a relatively rapid decline(9,)(10). So far, various models have been proposed to explain the afterglow emission, including a choked-jet cocoon(4,8,11-13) and a successful-jet cocoon(4,8,11-18) (also called a structured jet). However, the observational data have remained inconclusive(10,15,19,20) as to whether GW170817 launched a successful relativistic jet. Here we report radio observations using very long-baseline interferometry. We find that the compact radio source associated with GW170817 exhibits superluminal apparent motion between 75 days and 230 days after the merger event. This measurement breaks the degeneracy between the choked- and successful-jet cocoon models and indicates that, although the early-time radio emission was powered by a wide-angle outflow(8) (a cocoon), the late-time emission was most probably dominated by an energetic and narrowly collimated jet (with an opening angle of less than five degrees) and observed from a viewing angle of about 20 degrees. The imaging of a collimated relativistic outflow emerging from GW170817 adds substantial weight to the evidence linking binary neutron-star mergers and short -gamma-my bursts.