MOST small asteroids are thought to result from catastrophic collisions1, and their shapes can provide insight into their origin and collisional evolution. Two main-belt asteroids have been successfully imaged by spacecraft2,3, but such images have yet to be obtained for asteroids that cross Earth's orbit. Earth-crossing asteroids are generally too small to be resolved by optical telescopes, and shape constraints derived from optical lightcurves are subject to large systematic biases4. Ground-based radar observations, on the other hand, have proved successful in resolving the shapes of some small asteroids5-9. We describe here radar measurements of the Earth-crossing asteroid 1620 Geographos during its recent close encounter with the Earth. We have determined the silhouette of Geographos along its rotation axis, and confirm earlier lightcurve-based conjectures10 that this object has a very unusual shape. The silhouette is irregular, non-convex and has an aspect ratio of 2.76 +/- 0.21, establishing it as the most elongated Solar System object yet imaged. The unusual nature of the shape is underscored by laboratory fragmentation experiments11,12, in which the average aspect ratio of fragments is 1.4, with fewer than 1% as elongated as Geographos.