The small bodies in the Solar System are thought to have been highly affected by collisions and erosion. In the asteroid belt, direct evidence of the effects of large collisions can be seen in the existence of separate families of asteroids--a family consists of many asteroids with similar orbits and, frequently, similar surface properties, with each family being the remnant of a single catastrophic impact. In the region beyond Neptune, in contrast, no collisionally created families have hitherto been found. The third largest known Kuiper belt object, 2003 EL61, however, is thought to have experienced a giant impact that created its multiple satellite system, stripped away much of an overlying ice mantle, and left it with a rapid rotation. Here we report the discovery of a family of Kuiper belt objects with surface properties and orbits that are nearly identical to those of 2003 EL61. This family appears to be fragments of the ejected ice mantle of 2003 EL61.