We present results from a Chandra X-Ray Observatory study of the Ðeld X-ray source populations in four di †erent observations : two high-redshift (z D 0.5) clusters of galaxies 3C 295 and RX J003033.2]261819 ; and two noncluster Ðelds with similar exposure time. Surprisingly, the 0.5È2 keV source surface densities (D900È1200 sources deg~2 at a Ñux limit of 1.5 ] 10~15 ergs cm~2 s~1) measured in an D8@ ] 8@ area surrounding each cluster exceed by a factor of D2 the value expected on the basis of the ROSAT and Chandra log N-log S, with a signiÐcance of D2 p each, or D3.5 p when the two Ðelds are combined (i.e., a probability to be a statistical Ñuctuation of \1% and \0.04%, respectively). The same analysis performed on the noncluster Ðelds and on the outer chips of the cluster Ðelds does not show evidence of such an excess. In both cluster Ðelds, the summed 0.5È10 keV spectrum of the detected objects is well Ðtted by a power law with ! D 1.7 similar to active galactic nuclei (AGNs) and shows no sign of intrinsic absorption. The few (D10 of 35) optical identiÐcations available to date conÐrm 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 QSOs by the galaxy clusters. All explanations, however, are 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.