MOST galaxies, including our own, are located in groups(1). In the most compact galaxy groups, the members are separated on the sky by only a few galactic radii, and numerical simulations(2) suggest that such systems will merge to form a single elliptical galaxy (a ’fossil group’) in a few billion years. Recent observations(3,4) have shown that some compact groups are surrounded by X-ray-emitting haloes of hot gas, and have suggested that they contain substantial amounts of dark matter. An elliptical galaxy formed by the merger of such a group will retain its halo(4), which is unaffected by merging. Using recent X-ray observations from Rosat we have searched for fossil groups, and we report here the discovery of a possible candidate at a redshift of 0.171. This candidate has a high X-rays luminosity, comparable to those of the brighter compact groups(5) and appears similar to the giant elliptical galaxies at the centres of clusters, yet it is apparently isolated. Its optical properties are also consistent with an origin as the merged remains of a typical compact group.