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A subset of ultraluminous X-ray sources (those with luminosities < 10^40erg/s) are thought to be powered by the accretion of gas onto black holes withmasses of ~5-20 M_solar, probably via an accretion disc. The X-ray and radioemission are coupled in such Galactic sources, with the radio emissionoriginating in a relativistic jet thought to be launched from the innermostregions near the black hole, with the most powerful emission occurring when therate of infalling matter approaches a theoretical maximum (the Eddingtonlimit). Only four such maximal sources are known in the Milky Way, and theabsorption of soft X-rays in the interstellar medium precludes determining thecausal sequence of events that leads to the ejection of the jet. Here we reportradio and X-ray observations of a bright new X-ray source whose peak luminositycan exceed 10^39 erg/s in the nearby galaxy, M31. The radio luminosity isextremely high and shows variability on a timescale of tens of minutes, arguingthat the source is highly compact and powered by accretion close to theEddington limit onto a stellar mass black hole. Continued radio and X-raymonitoring of such sources should reveal the causal relationship between theaccretion flow and the powerful jet emission.

Bright radio emission from an ultraluminous stellar-mass microquasar in M31