Using balloon-borne instrumentation of very high sensitivity, we have detected approx.25 hard x-ray bursts with peak fluxes of above 7 x 10/sup -3/ (cm/sup 2/ s keV)/sup -1/ at 20 keV, in 141 minutes of observation of the Sun on 1980 June 27. These hard x-ray microflares last from a few seconds to several tens of seconds and have power-law energy spectra. They are generally accompanied by small soft x-ray bursts, but H..cap alpha.