The extreme densities(1) of neutron stars make them an ideal system in which to investigate the equation of state of nuclear matter; accurate determinations of neutron star masses and radii are crucial for this, Current observations of neutron stars in binary systems yield masses that are generally consistent with theory(2). But measurements of radii are more difficult as they require the detection of thermal radiation from the surface, which in general is masked by emission from non-thermal processes in radio pulsars(3) and X-ray binary systems(4). Isolated radio-quiet neutron stars’ offer the best opportunity to observe the surface thermal emission, Here we report the detection of the optical counterpart of a candidate isolated neutron star, RX J185635-3754 (ref. 6). Our optical flux data, combined with existing extreme ultraviolet(7) and X-ray(6) observations, show the spectrum to be approximately thermal. By adopting the upper bound to the distance of the source, and assuming a plausible model for the spectral energy distribution, we find that the radius of the object cannot exceed 14 km. This result is inconsistent with a number of recent equations of states proposed for neutron stars.