GW170817 is the first gravitational wave detection of a binary neutron star merger. It was accompanied by radiation across the electromagnetic spectrum and localized to the galaxy NGC 4993 at a distance of 40 Mpc. It has been proposed that the observed gamma-ray, X-ray and radio emission is due to an ultra-relativistic jet launched during the merger, directed away from our line of sight. The presence of such a jet is predicted from models positing neutron star mergers as the central engines driving short-hard gamma-ray bursts (SGRBs). Here we show that the radio light curve of GW170817 has no direct signature of an off-axis jet afterglow. While we cannot rule out the existence of a jet pointing elsewhere, the observed gamma-rays could not have originated from such a jet. Instead, the radio data requires a mildly relativistic wide-angle outflow moving towards us. This outflow could be the high velocity tail of the neutron-rich material dynamically ejected during the merger or a cocoon of material that breaks out when a jet transfers its energy to the dynamical ejecta. The cocoon scenario can explain the radio light curve of GW170817 as well as the gamma-rays and X-rays (possibly also ultraviolet and optical emission), and hence is the model most consistent with the observational data. Cocoons may be a ubiquitous phenomenon produced in neutron star mergers, giving rise to a heretofore unidentified population of radio, ultraviolet, X-ray and gamma-ray transients in the local universe.