We present low-resolution (64 < R < 124) mid-infrared (8--38 micron) Spitzer/IRS spectra of two z~1.3 ultraluminous infrared galaxies (LFIR~10^13) discovered in a Spitzer/MIPS survey of the Bootes 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 and a possible lensing amplification of <~10. The 6.2, 7.7, 11.3, and 12.8 micron PAH emission bands in its IRS spectrum indicate a redshift of z~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 [NeII]/[NeIII] 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~1.3. 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 ``redshift desert 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.
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