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We present results from a Chandra X-ray Observatory study of the field X-raysource populations in 4 different observations: two high-redshift (z~0.5)clusters of galaxies 3C295 and RXJ003033.2+261819; and two non-cluster fieldswith similar exposure time. Surprisingly, the 0.5-2 keV source surfacedensities (~900-1200 sources deg**-2 at a flux limit of 1.5x10**-15 ergcm**-2s**-1) measured in an ~8'x8' area surrounding each cluster exceed by afactor of ~2 the value expected on the basis of the ROSAT and ChandralogN-logS, with a significance of ~2 sigma each, or ~3.5 sigma when the 2fields are combined (i.e. a probability to be a statistical fluctuation of <1%and <0.04%, respectively). The same analysis performed on the non-clusterfields and on the outer chips of the cluster fields does NOT show evidence ofsuch an excess. In both cluster fields, the summed 0.5-10 keV spectrum of thedetected objects is well fitted by a power-law with Gamma~1.7 similar to AGNsand shows no sign of intrinsic absorption. The few (~10 out of 35) opticalidentifications available to date confirm that most of them are, as expected,AGNs but the number of redshifts available is too small to allow conclusions ontheir nature. We discuss possible interpretations of the overdensity in termsof: a statistical variation of Cosmic Background sources; a concentration ofAGNs and/or powerful starburst galaxies associated with the clusters; and gravitational lensing of background QSO's by the galaxy clusters. Allexplanations are however difficult to reconcile with the large number of excesssources detected. Deeper X-ray observations and more redshifts measurements areclearly required to settle the issue.Comment: 22 LateX pages (including Tables and Figures), uses psfig.sty and  emulateapj.sty. Accepted for publication in Astrophysical Journa

ChandraStudy of an Overdensity of X‐Ray Sources around Two Distant (z ∼ 0.5) Clusters