Massive black holes are believed to reside at the centres of most galaxies. They can be- come detectable by accretion of matter, either continuously from a large gas reservoir or impulsively from the tidal disruption of a passing star, and conversion of the gravitational energy of the infalling matter to light. Continuous accretion drives Active Galactic Nuclei (AGN), which are known to be variable but have never been observed to turn on or off. Tidal disruption of stars by dormant massive black holes has been inferred indirectly but the on- set of a tidal disruption event has never been observed. Here we report the first discovery of the onset of a relativistic accretion-powered jet in the new extragalactic transient, Swift J164449.3+573451. The behaviour of this new source differs from both theoretical models of tidal disruption events and observations of the jet-dominated AGN known as blazars. These differences may stem from transient effects associated with the onset of a powerful jet. Such an event in the massive black hole at the centre of our Milky Way galaxy could strongly ionize the upper atmosphere of the Earth, if beamed towards us.