  We present a new X-ray selected high redshift quasar CXOCY J125304.0-090737
at z=4.179, discovered by the Calan-Yale Deep Extragalactic Research (CYDER)
Survey. This quasar is the fifth X-ray selected high redshift radio quiet
quasar ($z>4$) found so far. Here, we present its observed properties which are
characterized by its relative optical and X-ray faintness, its X-ray hardness
and its X-ray strength compared to optically selected quasars at high redshift.
We also compare the X-ray selected high redshift radio quiet quasars to their
optically selected counterparts. We find that the optical to X-ray spectral
slope, $\alpha_{ox}$, is statistically harder (more X-ray luminous) for the
X-ray selected radio quiet quasars than for the optically selected ones. This
result, given the different range of rest frame ultraviolet luminosities
studied and the selection of the samples, is consistent with the previously
found correlation between X-ray and rest frame ultraviolet luminosities and
would extend that result to a much wider luminosity range at high redshift.
Finally, we discuss the prospects of unveiling the quasar luminosity function
at high redshifts using X-ray surveys. The discovery of a high redshift object
in the first field of our survey program provides suggestive evidence that
X-ray selected surveys may identify more such objects than would be expected
from an extrapolation of the optical luminosity function.
