In December 1990, • set of liquid-nitrogen-cooled germ•nium hard X-ray •nd g•mm•-r•y spectrometers w•s flown •bo•rd • high-altitude balloon from McMurdo, Antarctica, for solar, •strophysical, •nd terrestrial observations. This flight w•s the first circumnavigation (•9-d•y duration) of the Antarctic continent by • l•rge (800,000-cubic-meter) balloon. Bremsstrahlung h•rd X-ray emission extending up to •300 keV, from the precipitation of high-energy electrons, w•s observed on six separate occasions over the auroral zone, all during low geomagnetic •ctivity (K r _< 2+). All events were consistent with emission •t the tr•pping boundary; obserwtions over the polar c•p showed no precipitation. We present the first high-resolution (AE keV/full width hMf maximum (FWHM) spectra of this hard X-ray emission in the energy range 20-300 keV. The observed count spectra are deconvolved by model-independent techniques to photon spectra and then to the precipitating electron spectra. The spectral hardness shows an inverse relation with L as expected. Our results suggest that high-resolution spectroscopy could be extremely effective in characterizing electron precipitation if coupled with imaging capability. •> 50% of the time at invariant latitude 65 ø. The time-? averaged count rate for this common X-ray "drizzle" is about 15 (cma/sec) -1 integrated above 25 keV lAnderson, 1965]. Below this energy the atmosphere above the balloon absorbs most of the X-rays. In intense precipitation events, fluxes ranging up to ~200 (cma/sec) -1 have been seen [Anderson and Eriemark, 1960; Brown and Barcus, 1963]. The hard X-ray spectrum drops off rapidly in energy, generally disappearing below background by ~300 keV. The energetic electrons which create these hard X-rays Paper mtrnber 95JA01472. 0148-0227/95/95 JA-01472505.00 usually contain much less total energy than the softer (order of 1-10 keV) population of electrons responsible for visible aurorae.