The Great Observatories Origins Deep Survey (GOODS) combines deep HST and Spitzer imaging with the deepest Chandra/XMM observations to probe obscured AGN at higher redshifts than previous multiwavelength surveys. We present a self-consistent implementation of the AGN unification paradigm, which postulates obscured AGN wherever there are unobscured AGN, to successfully explain the infrared, optical, and X-ray number counts of X-ray sources detected in the GOODS fields. Assuming either a constant ratio of obscured to unobscured AGN of 3:1 (the local value), or a ratio that decreases with luminosity, and including Compton-thick sources, we can explain the spectral shape and normalization of the extragalactic X-ray "background" as a superposition of unresolved AGN, predominantly at z similar to 0.5-1.5 and L-x similar to 10(43)-10(44) ergs/s. The possible dependence of the obscured to unobscured ratio with redshift is not well constrained; present data allow it to decrease or increase substantially beyond z similar to 1.