THE population of asteroids that cross the Earth's orbit is responsible for most of the terrestrial impacts of kilometre-size objects, of which there may be several per million years1. About 150 Earth-crossing asteroids are known, although many more are thought to exist2. Asteroids that come close to the Earth's orbit, but do not currently cross it, may also pose a threat if they evolve onto Earth-crossing orbits. The asteroid 433 Eros, with a dia-meter of ~22 km and a perihelion of 1.13 AU (where 1 AU is the average distance of the Earth from the Sun), is the second-largest near-Earth asteroid3. Here we report a study of the dynamical evolution of Eros's orbit over a period of two million years. We identify an orbital resonance with Mars that has the potential to perturb Mars-crossing asteroids, such as Eros, onto Earth-crossing orbits; of eight trial orbits that closely match Eros's present orbital parameters, three become Earth-crossing on the timescale of our simulations, and one of these hits the Earth after 1.14 Myr. Although our simulations indicate no significant danger of a catastrophic impact by this large near-Earth asteroid during the next ~105 years, such a collision is likely in the far future.