Ultra-luminous X-ray sources are extragalactic objects located outside the nucleus of the host galaxy with bolometric luminosities >10^39 erg s^-1. These extreme luminosities - if the emission is isotropic and below the theoretical (i.e. Eddington) limit, where the radiation pressure is balanced by the gravitational pressure - imply the presence of an accreting black hole with a mass of ~10^2-10^5 times that of the Sun. The existence of such intermediate mass black holes is in dispute, and though many candidates have been proposed, none are widely accepted as definitive. Here we report the detection of a variable X-ray source with a maximum 0.2-10 keV luminosity of up to 1.2 x 10^42 erg s^-1 in the edge-on spiral galaxy ESO 243-49, with an implied conservative lower limit of the mass of the black hole of ~500 Msun. This finding presents the strongest observational evidence to date for the existence of intermediate mass black holes, providing the long sought after missing link between the stellar mass and super-massive black hole populations.
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