It has been suspected for nearly 50 years that galaxy clusters contain a population of intergalactic stars ripped from the galaxies during cluster formation, or when the galactic orbits pass through the cluster centre(1-3). Observational support for the existence of such a stellar population is provided both by measurements of the diffuse light in clusters(4-9), and by the recent detection of planetary nebulae with positions or velocities far removed from any observable cluster galaxy(10,11). But estimates for the mass of the diffuse population and its distribution relative to the cluster galaxies are still highly uncertain. Here we report the direct detection of intergalactic stars in deep images of a blank field in the Virgo cluster. The data suggest that these stars form approximately one-tenth of the total stellar mass of the cluster. We observe a relatively homogeneous distribution of stars, with evidence of a slight gradient towards M87.