We report on simultaneous observations of the local starburst system Arp 299 with NuSTAR and Chandra, which provides the first resolved images of this galaxy up to energies of ~ 45 keV. Fitting the 3-40 keV spectrum reveals a column density of $N_{rm H}$ ~ 4 x10^{24} cm^{-2}, characteristic of a Compton-thick AGN, and a 10-30 keV luminosity of 1.2x 10^{43} ergs s^{-1}. The hard X-rays detected by NuSTAR above 10 keV are centered on the western nucleus, Arp 299-B, which previous X-ray observations have shown to be the primary source of neutral Fe-K emission. Other X-ray sources, including Arp 299-A, the eastern nucleus which is also thought to harbor an AGN, as well as X-ray binaries, contribute $lesssim 10%$ to the 10-20 keV emission from the Arp 299 system. The lack of significant emission above 10 keV other than that attributed to Arp 299-B suggests that: a) any AGN in Arp 299-A must be heavily obscured ($N_{rm H}$ > 10^{24} cm^{-2}) or have a much lower luminosity than Arp 299-B and b) the extranuclear X-ray binaries have spectra that cut-off above ~10 keV. Such soft spectra are characteristic of ultraluminous X-ray (ULX) sources observed to date by NuSTAR.
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