Ultraluminous X-ray sources are extragalactic objects located outside the nucleus of the host galaxy with bolometric luminosities exceeding 10(39) erg s(-1). These extreme luminosities-if the emission is isotropic and below the theoretical (Eddington) limit, where the radiation pressure is balanced by the gravitational pressure-imply the presence of an accreting black hole with a mass of approximately 10(2)-10(5) solar masses (Msymbol: see text). 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 1.1 x 10(42) erg s(-1) in the edge-on spiral galaxy ESO 243-49, with an implied conservative lower limit for the mass of the black hole of approximately 500Msymbol: see text.