Galaxies had their most significant impact on the Universe when they assembled their first generations of stars. Energetic photons emitted by young, massive stars in primeval galaxies ionized the intergalactic medium surrounding their host galaxies, cleared sight-lines along which the light of the young galaxies could escape, and fundamentally altered the physical state of the intergalactic gas in the Universe continuously until the present day. Observations of the Cosmic Microwave Background, and of galaxies and quasars at the highest redshifts, suggest that the Universe was reionised through a complex process that was completed about a billion years after the Big Bang, by redshift z~6. Detecting ionizing Ly-alpha photons from increasingly distant galaxies places important constraints on the timing, location and nature of the sources responsible for reionisation. Here we report the detection of Ly-a photons emitted less than 600 million years after the Big Bang. UDFy-38135539 is at a redshift z=8.5549+-0.0002, which is greater than those of the previously known most distant objects, at z=8.2 and z=6.97. We find that this single source is unlikely to provide enough photons to ionize the volume necessary for the emission line to escape, requiring a significant contribution from other, probably fainter galaxies nearby.