Supermassive black holes have powerful gravitational fields with strong gradients that can destroy stars that get too close(1,2), producing a bright flare in ultraviolet and X-ray spectral regions from stellar debris that forms an accretion disk around the black hole(3-7). The aftermath of this process may have been seen several times over the past two decades in the form of sparsely sampled, slowly fading emission from distant galaxies(8-14), but the onset of the stellar disruption event has not hitherto been observed. Here we report observations of a bright X-ray flare from the extragalactic transient Swift J164449.3+573451. This source increased in brightness in the X-ray band by a factor of at least 10,000 since 1990 and by a factor of at least 100 since early 2010. We conclude that we have captured the onset of relativistic jet activity from a supermassive black hole. A companion paper(15) comes to similar conclusions on the basis of radio observations. This event is probably due to the tidal disruption of a star falling into a supermassive black hole, but the detailed behaviour differs from current theoretical models of such events.