We present high resolution (approx.1 keV FWHM) spectral measurements from 13 to 300 keV of a solar flare hard X-ray burst observed on 1980 June 27 by a balloon-borne array of cooled germanium planar detectors. At energies below approx.35 keV we identify a new component of solar flare hard X-rays. This component is characterized by an extremely steep spectrum which fits closely to that from a Maxwellian electron distribution with a maximum temperature of approx.34 x 10/sup 6/ K and an emission measure of 2.9 x 10/sup 48/ cm/sup -3/. This hot isothermal component appears at the peak of the normal power-law-like impulsive X-ray burst component, and it remains isothermal and dominates the X-ray emission below approx.30 keV through the decay of the flare event.