We present the high-redshift (3 <z < 5.3) 0.5-2 keV number counts and the 2-10 keV (rest-frame) space density of X-ray-selected active galactic nuclei (AGNs) detected in the Chandra Cosmic Evolution Survey. The sample comprises 81 X-ray-detected sources with available spectroscopic (31) and photometric (50) redshifts plus 20 sources with a formal z phot < 3 but with a broad photometric redshift probability distribution, such that z phot + 1σ > 3. Eighty-one sources are selected in the 0.5-2 keV band, fourteen are selected in the 2-10 keV and six in the 0.5-10 keV bands. We sample the high-luminosity (log L (2-10 keV) > 44.15 erg s–1) space density up to z ~ 5 and a fainter luminosity range (43.5 erg s–1 < log L (2-10 keV) < 44.15 erg s–1) than previous studies, up to z = 3.5. We weighted the contribution to the number counts and the space density of the sources with photometric redshift by using their probability of being at z > 3. We find that the space density of high-luminosity AGNs declines exponentially at all the redshifts, confirming the trend observed for optically selected quasars. At lower luminosity, the measured space density is not conclusive, and a larger sample of faint sources is needed. Comparisons with optical luminosity functions and black hole formation models are presented together with prospects for future surveys.