  Using the Infrared Spectrograph on board the Spitzer Space Telescope, we
present low-resolution (64 < lambda / dlambda < 124), mid-infrared (20-38
micron) spectra of 23 high-redshift ULIRGs detected in the Bootes field of the
NOAO Deep Wide-Field Survey. All of the sources were selected to have 1) fnu(24
micron) > 0.5 mJy; 2) R-[24] > 14 Vega mag; and 3) a prominent rest-frame 1.6
micron stellar photospheric feature redshifted into Spitzer's 3-8 micron IRAC
bands. Of these, 20 show emission from polycyclic aromatic hydrocarbons (PAHs),
usually interpreted as signatures of star formation. The PAH features indicate
redshifts in the range 1.5 < z < 3.0, with a mean of <z>=1.96 and a dispersion
of 0.30. Based on local templates, these sources have extremely large infrared
luminosities, comparable to that of submillimeter galaxies. Our results confirm
previous indications that the rest-frame 1.6 micron stellar bump can be
efficiently used to select highly obscured starforming galaxies at z~2, and
that the fraction of starburst-dominated ULIRGs increases to faint 24 micron
flux densities. Using local templates, we find that the observed narrow
redshift distribution is due to the fact that the 24 micron detectability of
PAH-rich sources peaks sharply at z = 1.9. We can analogously explain the
broader redshift distribution of Spitzer-detected AGN-dominated ULIRGs based on
the shapes of their SEDs. Finally, we conclude that z~2 sources with a
detectable 1.6 micron stellar opacity feature lack sufficient AGN emission to
veil the 7.7 micron PAH band.
