The Circinus galaxy is one of the closest obscured active galactic nuclei (AGNs), making it an ideal target for detailed study. Combining archival Chandra and XMM-Newton data with new NuSTAR observations, we model the 2-79 keV spectrum to constrain the primary AGN continuum and to derive physical parameters for the obscuring material. Chandra's high angular resolution allows a separation of nuclear and off-nuclear galactic emission. In the off-nuclear diffuse emission, we find signatures of strong cold reflection, including high equivalent-width neutral Fe lines. This Compton-scattered off-nuclear emission amounts to 18% of the nuclear flux in the Fe line region, but becomes comparable to the nuclear emission above 30 keV. The new analysis no longer supports a prominent transmitted AGN component in the observed band. We find that the nuclear spectrum is consistent with Compton scattering by an optically thick torus, where the intrinsic spectrum is a power law of photon index Gamma = 2.2-2.4, the torus has an equatorial column density of N sub(H) = (6-10) x 10 super(24) cm super(-2), and the intrinsic AGN 2-10 keV luminosity is (2.3-5.1) x 10 super(42) erg s super(-1). These values place Circinus along the same relations as unobscured AGNs in accretion rate versus Gamma and L sub(x) versus L sub(TR) phase space. NuSTAR's high sensitivity and low background allow us to study the short timescale variability of Circinus at X-ray energies above 10 keV for the first time. The lack of detected variability favors a Compton-thick absorber, in line with the spectral fitting results.