Supernovae resulting from the deaths of massive stars span a wide range of peak luminosities, usually reached within 30 days after explosion. Their diversity depends on the star’s initial mass and rate of mass loss during its lifetime. Stars born with initial masses above 40 times the mass of the Sun are expected to shed their hydrogen envelopes to expose their He core before they die, resulting in supernovae with little or no evidence for hydrogen gas observed in their spectrum. Here we report on our discovery and follow-up observations of SN 2006gy, which reveal that it reached a peak luminosity at least 3 times greater than any other supernova seen to date, and far greater than most others. We find that a large ejected mass of order 100 Solar masses is required to power its enormous total radiated luminosity, indicating a total kinetic energy of more than 10 ergs. This suggests that SN 2006gy marked the demise of an extremely massive star that, contrary to expectations, failed to shed its massive hydrogen envelope. A circumstellar shell that surrounded the progenitor star has a large mass and expansion speed, effectively ruling-out certain types of progenitor stars. Based on a number of lines of evidence, we suggest that the progenitor was a very massive evolved object like eta Carinae, which is the most luminous star known in the Milky Way. These observations suggest that the most massive stars can explode earlier than expected, and can create bright supernovae instead of dying ignominious deaths through direct collapse to a black hole. If such a fate is common, then supernovae from the first stars in the universe, which may have been extremely massive, will be more numerous than previously believed.