Massive black holes are generally thought to exist at the centres of galaxies, but an unambiguous identification of a black hole has been impeded by a lack of evidence for the strong-field relativistic effects expected in the vicinity of such an object. Several years ago, a very broad iron emission line was discovered in the active galaxy MCG-6-30-15, indicative of emission from an accretion disk near the event horizon of a black hole. But this interpretation, based on the line profile, was somewhat model dependent (refs 2-5). Here we present an analysis of the iron-line emission from MCG-6-30-15 that is insensitive to the details (for example, diskthickness and emissivity) of the disk model used. We find that the inner edge of the disk material giving rise to the line is within 2.6 +/- 0.3 times the Schwarzschild radius-the event horizon of a non-rotating black hole-at the 95% confidence level. Changes to the disk parameters can only decrease the inner radius of the emitting region, and so we can be confident that we are observing emission from gravitationally bound material in the strong-field region of a supermassive black hole. Moreover, we find that the black hole is rotating at a rate which is ≳23 +/- 17% of the theoretical maximum, although this conclusion is model dependent.