Aims. We study the spectral properties of the unresolved cosmic X-ray background (CXRB) in the 1.5–7.0 keV energy band with the aim of providing an observational constraint on the statistical properties of those sources that are too faint to be individually probed. Methods. We made use of the Swift X-ray observation of the Chandra deep field South complemented by the Chandra data. Exploiting the lowest instrument background (Swift) together with the deepest observation ever performed (Chandra) we measured the unresolved emission at the deepest level and with the best accuracy available today. Results. We find that the unresolved CXRB emission can be modeled by a single power law with a very hard photon index Γ = 0.1 ± 0.7 and a flux of 5-2.6+3.2 erg s-1 cm-2 deg-2 in the 2.0–10 keV energy band (1σ error). Thanks to the low instrument background of the Swift-XRT, we significantly improved the accuracy with respect to previous measurements. Conclusions. These results point towards a novel ingredient in AGN population synthesis models, namely a positive evolution of the Compton-thick AGN population from local Universe to high redshift.