  We present a NuSTAR, Chandra, and XMM--Newton survey of nine of the nearest
ultraluminous infrared galaxies (ULIRGs). The unprecedented sensitivity of
NuSTAR at energies above 10 keV enables spectral modeling with far better
precision than was previously possible. Six of the nine sources observed were
detected sufficiently well by NuSTAR to model in detail their broadband X-ray
spectra, and recover the levels of obscuration and intrinsic X-ray
luminosities. Only one source (IRAS 13120--5453) has a spectrum consistent with
a Compton--thick AGN, but we cannot rule out that a second source (Arp 220)
harbors an extremely highly obscured AGN as well. Variability in column density
(reduction by a factor of a few compared to older observations) is seen in IRAS
05189--2524 and Mrk 273, altering the classification of these border-line
sources from Compton-thick to Compton-thin. The ULIRGs in our sample have
surprisingly low observed fluxes in high energy (>10 keV) X-rays, especially
compared to their bolometric luminosities. They have lower ratios of unabsorbed
2--10 keV to bolometric luminosity, and unabsorbed 2--10 keV to mid-IR [O IV]
line luminosity than do Seyfert 1 galaxies. We identify IRAS 08572+3915 as
another candidate intrinsically X-ray weak source, similar to Mrk 231. We
speculate that the X-ray weakness of IRAS 08572+3915 is related to its powerful
outflow observed at other wavelengths.
