We report the discovery of fast , frequency-dependent intensity variations from the scintillating intra-day variable quasar J1819 + 3845 at \lambda 21 cm which resemble diffractive interstellar scintillations observed in pulsars . The observations were taken with the Westerbork Synthesis Radio Telescope on a dozen occasions in the period between Aug 2002 and Jan 2005 . The data were sampled at both high temporal and high frequency resolution and have an overall simultaneous frequency span of up to 600 MHz . In constructing the light curves and dynamic spectra the confusion from background sources has been eliminated . The timescale ( down to 20 min ) and the bandwidth ( frequency decorrelation bandwidth of 160 MHz ) of the observed variations jointly imply that the component of the source exhibiting this scintillation must possess a brightness temperature well in excess of the inverse Compton limit . A specific model in which both the source and scintillation pattern are isotropic implies a brightness temperature 0.5 \times 10 ^ { 13 } z _ { pc } K , where previous estimates place the distance to the scattering medium in the range z _ { pc } = 4 - 12 pc , yielding a minimum brightness temperature > 20 times the inverse Compton limit . An independent estimate of the screen distance using the 21 cm scintillation properties alone indicates a minimum screen distance of z \approx 40 pc and a brightness temperature above 2 \times 10 ^ { 14 } K. There is no evidence for anisotropy in the scattering medium or source from the scintillation characteristics , but these estimates may be reduced by a factor comparable to the axial ratio if the source is indeed elongated . The observed scintillation properties of J1819 + 3845 at 21 cm are compared with those at 6 cm , where a significantly larger source size has been deduced for the bulk of the emission by Dennett-Thorpe & de Bruyn ( 2003 ) . However , opacity effects within the source and the different angular scales probed in the regimes of weak and strong scattering complicate this comparison .