  We present a new measurement of the space density of high redshift
(3.0<z<4.5), X-ray selected QSOs obtained by exploiting the deep and uniform
multiwavelength coverage of the COSMOS survey. We have assembled a
statistically large (40 objects), X-ray selected (F_{0.5-2 keV} >10^{-15} cgs),
homogeneous sample of z>3 QSOs for which spectroscopic (22) or photometric (18)
redshifts are available. We present the optical (color-color diagrams) and
X-ray properties, the number counts and space densities of the z>3 X-ray
selected quasars population and compare our findings with previous works and
model predictions. We find that the optical properties of X-ray selected
quasars are not significantly different from those of optically selected
samples. There is evidence for substantial X-ray absorption (logN_H>23 cm^{-2})
in about 20% of the sources in the sample. The comoving space density of
luminous (L_X >10^{44} erg s^-1) QSOs declines exponentially (by an e--folding
per unit redshift) in the z=3.0-4.5 range, with a behavior similar to that
observed for optically bright unobscured QSOs selected in large area optical
surveys. Prospects for future, large and deep X-ray surveys are also discussed.
