We report the detection of emission from a non-thermal electron distribution in a small solar microflare ( GOES class A5.7 ) observed by the Nuclear Spectroscopic Telescope Array ( NuSTAR ) , with supporting observation by the Reuven Ramaty High Energy Solar Spectroscopic Imager ( RHESSI ) . The flaring plasma is well accounted for by a thick-target model of accelerated electrons collisionally thermalizing within the loop , akin to the “ coronal thick target ” behavior occasionally observed in larger flares . This is the first positive detection of non-thermal hard X-rays from the Sun using a direct imager ( as opposed to indirectly imaging instruments ) . The accelerated electron distribution has a spectral index of 6.3 \pm 0.7 , extends down to at least 6.5 keV , and deposits energy at a rate of \sim 2 \times 10 ^ { 27 } erg s ^ { -1 } , heating the flare loop to at least 10 MK . The existence of dominant non-thermal emission in X-rays down to < 5 keV means that RHESSI emission is almost entirely non-thermal , contrary to what is usually assumed in RHESSI spectroscopy . The ratio of non-thermal to thermal energies is similar to that of large flares , in contrast to what has been found in previous studies of small RHESSI flares . We suggest that a coronal thick target may be a common property of many small microflares based on the average electron energy and collisional mean free path . Future observations of this kind will enable understanding of how flare particle acceleration changes across energy scales , and will aid the push toward the observational regime of nanoflares , which are a possible source of significant coronal heating .