The microquasar 1E1740.7-2942, also known as the "Great Annihilator," was observed by NuSTAR in the summer of 2012. We have analyzed in detail two observations taken ∼2 weeks apart, for which we measure hard and smooth spectra typical of the low/hard state. A few weeks later the source flux declined significantly. Nearly simultaneous coverage by INTEGRAL is available from its Galactic Center monitoring campaign lasting ∼2.5 months. These data probe the hard state spectrum from 1E1740.7-2942 before the flux decline. We find good agreement between the spectra taken with IBIS/ISGRI and NuSTAR, with the measurements being compatible with a change in flux with no spectral variability. We present a detailed analysis of the NuSTAR spectral and timing data and upper limits for reflection of the high energy emission. We show that the high energy spectrum of this X-ray binary is well described by thermal Comptonization. © 2014. The American Astronomical Society. All rights reserved.