  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.
