Near-Earth asteroids range in size from a few metres to more than 30 km : in addition to playing an important role in past and present impact rates on the Earth, they might one day be exploited as bases for space exploration or as mineral resources. Many near-Earth asteroids move on orbits crossing that of the Earth, but none has hitherto been identified as a dynamical companion to the Earth. Here we show that the orbit of asteroid 3753 (1986 TO), when viewed in the reference frame centred on the Sun but orbiting with the Earth, has a distinctive shape characteristic of ’horseshoe’ orbits. Although horseshoe orbits are a well-known feature of the gravitational three-body problem(1), the only other examples of objects moving on such orbits are the saturnian satellites Janus and Epimetheus(2)-and their behaviour is much less intricate than that of 3753. Moreover, the fact that 3753 exhibits such a dynamical relationship with the Earth shows that, although it is not a satellite of our planet per se, it is, apart from the Moon, the only known natural companion of the Earth.