Non-synchronous rotation of Europa was predicted on theoretical grounds, by considering the orbitally averaged torque exerted by Jupiter on the satellite's tidal bulges. If Europa's orbit were circular, or the satellite were comprised of a frictionless fluid without tidal dissipation, this torque would average to zero. However, Europa has a small forced eccentricity e ~ 0.01 (ref. 2), generated by its dynamical interaction with Io and Ganymede, which should cause the equilibrium spin rate of the satellite to be slightly faster than synchronous. Recent gravity data suggest that there may be a permanent asymmetry in Europa's interior mass distribution which is large enough to offset the tidal torque; hence, if non-synchronous rotation is observed, the surface is probably decoupled from the interior by a subsurface layer of liquid or ductile ice. Non-synchronous rotation was invoked to explain Europa's global system of lineaments and an equatorial region of rifting seen in Voyager images,. Here we report an analysis of the orientation and distribution of these surface features, based on initial observations made by the Galileo spacecraft. We find evidence that Europa spins faster than the synchronous rate (or did so in the past), consistent with the possibility of a global subsurface ocean.