We identify a population of 640 obscured and 839 unobscured AGNs at redshifts 0.7<z<~3 using multiwavelength observations of the 9 deg^2 NOAO Deep Wide-Field Survey (NDWFS) region in Bootes. We select AGNs on the basis of Spitzer IRAC colors obtained by the IRAC Shallow Survey. Redshifts are obtained from optical spectroscopy or photometric redshift estimators. We classify the IR-selected AGNs as IRAGN 1 (unobscured) and IRAGN 2 (obscured) using a simple criterion based on the observed optical to mid-IR color, with a selection boundary of R-[4.5]=6.1, where R and [4.5] are the Vega magnitudes in the R and IRAC 4.5 micron bands, respectively. We verify this selection using X-ray stacking analyses with data from the Chandra XBootes survey, as well as optical photometry from NDWFS and spectroscopy from MMT/AGES. We show that (1) these sources are indeed AGNs, and (2) the optical/IR color selection separates obscured sources (with average N_H~3x10^22 cm^-2 obtained from X-ray hardness ratios, and optical colors and morphologies typical of galaxies) and unobscured sources (with no X-ray absorption, and quasar colors and morphologies), with a reliability of >~80%. The observed numbers of IRAGNs are comparable to predictions from previous X-ray, optical, and IR luminosity functions, for the given redshifts and IRAC flux limits. We observe a bimodal distribution in R-[4.5] color, suggesting that luminous IR-selected AGNs have either low or significant dust extinction, which may have implications for models of AGN obscuration.
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