Using the Infrared Spectrograph on board the Spitzer Space Telescope , we present low-resolution ( 64 < \lambda / \delta \lambda < 124 ) , mid-infrared ( 20–38 \micron ) spectra of 23 high-redshift ULIRGs detected in the Boötes field of the NOAO Deep Wide-Field Survey . All of the sources were selected to have 1 ) ~ { } f _ { \nu } ( 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 \langle z \rangle = 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 \approx 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 \approx 2 sources with a detectable 1.6 \micron stellar opacity feature lack sufficient AGN emission to veil the 7.7 \micron PAH band .