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We report on observations of NGC1068 with NuSTAR, which provide the bestconstraints to date on its $>10$~keV spectral shape. We find no strongvariability over the past two decades, consistent with its Compton-thick AGNclassification. The combined NuSTAR, Chandra, XMM-Newton, and Swift-BATspectral dataset offers new insights into the complex reflected emission. Thecritical combination of the high signal-to-noise NuSTAR data and a spatialdecomposition with Chandra allow us to break several model degeneracies andgreatly aid physical interpretation. When modeled as a monolithic (i.e., asingle N_H) reflector, none of the common Compton-reflection models are able tomatch the neutral fluorescence lines and broad spectral shape of the Comptonreflection. A multi-component reflector with three distinct column densities(e.g., N_H~1.5e23, 5e24, and 1e25 cm^{-2}) provides a more reasonable fit tothe spectral lines and Compton hump, with near-solar Fe abundances. In thismodel, the higher N_H components provide the bulk of the Compton hump fluxwhile the lower N_H component produces much of the line emission, effectivelydecoupling two key features of Compton reflection. We note that ~30% of theneutral Fe Kalpha line flux arises from >2" (~140 pc), implying that asignificant fraction of the <10 keV reflected component arises from regionswell outside of a parsec-scale torus. These results likely have ramificationsfor the interpretation of poorer signal-to-noise observations and/or moredistant objects [Abridged].

NuSTAR Spectroscopy of Multi-Component X-ray Reflection from NGC 1068