We have surveyed a field covering 9.0 degrees^2 within the NOAO Deep Wide-Field Survey region in Bootes with the Multiband Imaging Photometer on the Spitzer Space Telescope (SST) to a limiting 24 um flux density of 0.3 mJy. Thirty one sources from this survey with F(24um) > 0.75 mJy which are optically very faint (R > 24.5 mag) have been observed with the low-resolution modules of the Infrared Spectrograph on SST. Redshifts derived primarily from strong silicate absorption features are reported here for 17 of these sources; 10 of these are optically invisible (R > 26 mag), with no counterpart in B_W, R, or I. The observed redshifts for 16 sources are 1.7 < z < 2.8. These represent a newly discovered population of highly obscured sources at high redshift with extreme infrared to optical ratios. Using IRS spectra of local galaxies as templates, we find that a majority of the sources have mid-infrared spectral shapes most similar to ultraluminous infrared galaxies powered primarily by AGN. Assuming the same templates also apply at longer wavelengths, bolometric luminosities exceed 10^13 L(solar).
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