It is now over 40 years since radio observations of neutral hydrogen revealed(1) the gaseous disk of our Galaxy to be warped. Subsequently, the warp has been detected in the distribution of Galactic dust(2), molecular clouds(3), and luminous stars(4,5). Roughly half of all spiral galaxies have similarly warped disks, which suggests that warps are a common and long-lived phenomenon. However, there is still no consensus as to what induces galactic disks to become warped : intergalactic winds, tidal interactions with satellites, magnetic pressure and massive dark haloes have all been proposed as causative agents. Here we use data from the Hipparcos satellite(6) to determine the small stellar motions in the plane of the sky (proper motions) that should accompany the warp, but which are undetectable in the gas. We find that although the spatial distribution of the stars is in line with previous studies of hydrogen, the velocity distribution has the opposite sign to that expected. Finding a plausible explanation of this result may be the key to solving the long-standing puzzle posed by galactic warps.