Since the 1995 discovery of the broad iron K-line emission from the Seyfert galaxy MCG-6-30-15 (ref. 1), broad iron K lines have been found in emission from several other Seyfert galaxies, from accreting stellar-mass black holes and even from accreting neutron stars. The iron K line is prominent in the reflection spectrum created by the hard-X-ray continuum irradiating dense accreting matter. Relativistic distortion of the line makes it sensitive to the strong gravity and spin of the black hole. The accompanying iron L-line emission should be detectable when the iron abundance is high. Here we report the presence of both iron K and iron L emission in the spectrum of the narrow-line Seyfert 1 galaxy 1H 0707-495. The bright iron L emission has enabled us to detect a reverberation lag of about 30 s between the direct X-ray continuum and its reflection from matter falling into the black hole. The observed reverberation timescale is comparable to the light-crossing time of the innermost radii around a supermassive black hole. The combination of spectral and timing data on 1H 0707-495 provides strong evidence that we are witnessing emission from matter within a gravitational radius, or a fraction of a light minute, from the event horizon of a rapidly spinning, massive black hole.