We present results from a Chandra X-ray Observatory study of the field X-ray source populations in 4 different observations : two high-redshift ( z \sim 0.5 ) clusters of galaxies 3C295 and RXJ003033.2+261819 ; and two non-cluster fields with similar exposure time . Surprisingly , the 0.5-2 keV source surface densities ( \sim 900-1200 sources deg ^ { -2 } at a flux limit of 1.5 \times 10 ^ { -15 } erg cm ^ { -2 } s ^ { -1 } ) measured in an \sim 8 ^ { \prime } \times 8 ^ { \prime } area surrounding each cluster exceed by a factor of \sim 2 the value expected on the basis of the ROSAT and Chandra logN-logS , with a significance of \sim 2 \sigma each , or \sim 3.5 \sigma when the 2 fields are combined ( i.e . a probability to be a statistical fluctuation of < 1 % and < 0.04 % , respectively ) . The same analysis performed on the non-cluster fields and on the outer chips of the cluster fields does not show evidence of such an excess . In both cluster fields , the summed 0.5-10 keV spectrum of the detected objects is well fitted by a power-law with \Gamma \sim 1.7 similar to AGNs and shows no sign of intrinsic absorption . The few ( \sim 10 out of 35 ) optical identifications available to date confirm that most of them are , as expected , AGNs but the number of redshifts available is too small to allow conclusions on their nature . We discuss possible interpretations of the overdensity in terms of : a statistical variation of Cosmic Background sources ; a concentration of AGNs and/or powerful starburst galaxies associated with the clusters ; and gravitational lensing of background QSO ’ s by the galaxy clusters . All explanations are however difficult to reconcile with the large number of excess sources detected . Deeper X-ray observations and more redshifts measurements are clearly required to settle the issue . Subject Headings : galaxies : active : clustering : general - X-rays : general