We present an analysis of a ~160 ks NuSTAR observation of the nearby bright Seyfert galaxy IC 4329A. The highquality broadband spectrum enables us to separate the effects of distant reflection from the direct coronal continuum, and to therefore accurately measure the high-energy cutoff to be Ecut = 178-40+74 keV. The coronal emission arises from accretion disk photons Compton up-scattered by a thermal plasma, with the spectral index and cutoff being due to a combination of the finite plasma temperature and optical depth. Applying standard Comptonization models, we measure both physical properties independently using the best signal to noise obtained to date in an active galactic nucleus over the 3-79 keV band. We derive kTe = 37-6+7 keV with τ = 1.25-0.10+0.20 assuming a slab geometry for the plasma, and kTe = 33-6+6 keV with τ = 3.41-0.38+0.58 for a spherical geometry, with both having an equivalent goodness-of-fit.