The asteroid 2002 VE68 is currently a quasi-satellite of Venus, the first object of this dynamical class to be discovered, and is also the first known co-orbital companion to Venus. Our computations show that it has been in its present orbital state for about seven millennia and will stay there for five more centuries to come. It has a high eccentricity (~ 0.4) and inclination (~ 9°). Consequently the maximum distance of the asteroid from the Sun is near that of the Earth and the minimum distance is smaller than the aphelion of Mercury. Very close approaches with Venus and Mercury are excluded within the interval of time of reliable numerical computation of the orbit, but repeated encounters with the Earth do occur. From the evolution of the orbit of this object, we conclude that it may have been a near-Earth asteroid, which, some 7000 yr ago, was injected into its present orbit by the action of the Earth.