It is currently unknown whether the Universe was reionized by quasars or stars at z>5. We point out that quasars can be best distinguished from stellar systems by their X-ray emission. Based on a simple hierarchical CDM model, we predict the number counts and X-ray fluxes of quasars at high redshifts. The model is consistent with available data on the luminosity function of high-redshift quasars in the optical and soft X-ray bands. The cumulative contribution of faint, undetected quasars in our model is consistent with the unresolved fraction of the X-ray background. We find that the Chandra X-ray Observatory might detect approximately 100 quasars from redshifts z>5 per its 17’x17’ field of view at the flux threshold of 2x10^-16 erg/s/cm^2. The redshifts of these faint point-sources could be identified by follow-up infrared observations from the ground or with the Next Generation Space Telescope.

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