We have identified an extremely luminous radio and X-ray source with an optically variable emission-line object in the outskirts of the nearby barred spiral galaxy NGC 1313. Archival data show that the object (officially designated SN 1978K) had a major optical outburst (MB < -12.3) in mid-1978 and that a radio and X-ray outburst followed this event. The light curve, optical spectra, radio data, and the X-ray data all indicate that the event was a very unusual Type II supernova, with many similar properties to the so-called Type V supernovae SN 1961V in NGC 1058 and SN 1986J in NGC 891. The currently bright Doppler-broadened Balmer lines, the forbidden lines and the extremely high radio and X-ray luminosities (among the brightest of known supernovae in both regimes) are believed to be powered by the shock driving through a dense circumstellar medium created by extreme mass-loss (∼4 × 10-5 Msun yr-1) from a massive progenitor. Some of the optical properties may be explained by the super outburst of an ?I Carinae-type object, but such an event would fail to explain the radio and X-ray luminosity. The closeness, low extinction and low confusion toward SN 1978K will allow for a detailed study of a class of peculiar supernovae which is possibly much more common than previously supposed.