Observations with Spitzer Space Telescope have recently revealed a significant population of high-redshift z~2 dust-obscured galaxies (DOGs) with large mid-IR to UV luminosity ratios. These galaxies have been missed in traditional optical studies of the distant universe. We present a simple method for selecting this high-z population based solely on the ratio of the observed mid-IR 24um to optical R-band flux density. In the 8.6 sq.deg Bootes NDWFS Field, we uncover ~2,600 DOG candidates (= 0.089/sq.arcmin) with 24um flux densities F24>0.3mJy and (R-[24])>14 (i.e., F[24]/F[R] > 1000). These galaxies have no counterparts in the local universe, and become a larger fraction of the population at fainter F24, representing 13% of the sources at 0.3~mJy. DOGs exhibit evidence of both star-formation and AGN activity, with the brighter 24um sources being more AGN- dominated. We have measured spectroscopic redshifts for 86 DOGs, and find a broad z distribution centered at <z>~2.0. Their space density is 2.82E-5 per cubic Mpc, similar to that of bright sub-mm-selected galaxies at z~2. These redshifts imply very large luminosities LIR>~1E12-14 Lsun. DOGs contribute ~45-100% of the IR luminosity density contributed by all z~2 ULIRGs, suggesting that our simple selection criterion identifies the bulk of z~2 ULIRGs. DOGs may be the progenitors of ~4L* present-day galaxies seen undergoing a luminous,short- lived phase of bulge and black hole growth. They may represent a brief evolution phase between SMGs and less obscured quasars or galaxies. [Abridged]
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