We have used archival Chandra and XMM-Newton observations of quasars hosting intrinsic narrow UV absorption lines (intrinsic NALs) to carry out an exploratory survey of their X-ray properties. Our sample consists of three intrinsic-NAL quasars and one mini-BAL quasar, plus four quasars without intrinsic absorption lines for comparison. These were drawn in a systematic manner from an optical/UV-selected sample. The X-ray properties of intrinsic-NAL quasars are indistinguishable from those of normal quasars. We do not find any excess absorption in quasars with intrinsic NALs, with upper limits of a few times 10^22 cm^-2. We compare the X-ray and UV properties of our sample quasars by plotting the equivalent width and blueshift velocity of the intrinsic NALs and the X-ray spectral index against the optical-to-X-ray slope, alpha-ox. When BAL quasars and other AGNs with intrinsic NALs are included, the plots suggest that intrinsic-NAL quasars form an extension of the BAL sequences and tend to bridge the gap between BAL and normal quasars. Observations of larger samples of intrinsic-NAL quasars are needed to verify these conclusions. We also test two competing scenarios for the location of the NAL gas in an accretion-disk wind. Our results strongly support a location of the NAL gas at high latitudes above the disk, closer to the disk axis than the dense BAL wind. We detect excess X-ray absorption only in Q0014+8118, which does not host intrinsic NALs. The absorbing medium very likely corresponds to an intervening system at z=1.1, which also produces strong absorption lines in the rest-frame UV spectrum of this quasar. In the appendix we discuss the connection between UV and X-ray attenuation and its effect on alpha-ox.
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