We have observed profound variability in the radio flux density of the quasar PKS 0405–385 on timescales of less than an hour ; this is unprecedented amongst extragalactic sources . If intrinsic to the source , these variations would imply a brightness temperature { T _ { B } \sim 10 ^ { 21 } K } , some nine orders of magnitude larger than the inverse Compton limit for a static synchrotron source , and still a million times greater than can be accommodated with bulk relativistic motion at a Lorentz factor \gamma \sim 10 . The variability is intermittent with episodes lasting a few weeks to months . Our data can be explained most sensibly as interstellar scintillation of a source component which is < 5 \mu arcsec in size — a source size which implies a brightness temperature { T _ { B } > 5 \times 10 ^ { 14 } K } , still far above the inverse Compton limit . Simply interpreted as a steady , relativistically beamed synchrotron source , this would imply a bulk Lorentz factor \gamma \sim 10 ^ { 3 } .