We present low-resolution ( 64 < R < 124 ) mid-infrared ( 8–38 \micron ) spectra of two z \approx 1.3 ultraluminous infrared galaxies with { L } _ { 8 - 1000 \micron } \approx 10 ^ { 13 } \ > { L _ { \odot } } : MIPS J142824.0+352619 and SST24 J142827.19+354127.71 . The spectra were taken with the Infrared Spectrograph ( IRS ) on board the Spitzer Space Telescope . Both objects were discovered in a Spitzer / MIPS survey of the Boötes field of the NOAO Deep Wide-Field Survey ( NDWFS ) . MIPS J142824.0+352619 is a bright 160 \micron source with a large infrared-to-optical flux density ratio . Previous authors provide evidence for a foreground lens and estimate an amplification of \lesssim 10 , although this factor is presently poorly constrained . The 6.2 , 7.7 , 11.3 , and 12.8 \micron PAH emission bands in its IRS spectrum indicate a redshift of z \approx 1.3 . The large equivalent width of the 6.2 \micron PAH feature indicates that at least 50 % of the mid-infrared energy is generated in a starburst , an interpretation that is supported by a large [ Ne ii ] / [ Ne iii ] ratio and a low upper limit on the X-ray luminosity . SST24 J142827.19+354127.71 has the brightest 24 \micron flux ( 10.55 mJy ) among optically faint ( R > 20 ) galaxies in the NDWFS . Its mid-infrared spectrum lacks emission features , but the broad 9.7 \micron silicate absorption band places this source at z \approx 1.3 . Optical spectroscopy confirms a redshift of z = 1.293 \pm 0.001 . Given this redshift , SST24 J142827.19+354127.71 has among the largest rest-frame 5 \micron luminosities known . The similarity of its SED to those of known AGN-dominated ULIRGs and its lack of either PAH features or large amounts of cool dust indicate that the powerful mid-infrared emission is dominated by an active nucleus rather than a starburst . Our results illustrate the power of the IRS in identifying massive galaxies in the well-known “ redshift desert ” between 1 < z < 2 and in discerning their power sources . Because they are bright , MIPS J142824.0+352619 ( pending future observations to constrain its lensing amplification ) and SST24 J142827.19+354127.71 are useful z > 1 templates of a high luminosity starburst and AGN , respectively .