We present Chandra observations of nine high-redshift quasars (z=2.7-5.9) discovered by the Sloan Digital Sky Survey with weak or undetectable high-ionization emission lines in their UV spectra (WLQs). Adding archival X-ray observations of six additional sources of this class has enabled us to place the strongest constraints yet on the X-ray properties of this remarkable class of AGNs. Although our data cannot rule out the possibility that the emission lines are overwhelmed by a relativistically boosted continuum, as manifested by BL Lac objects, we find that WLQs are considerably weaker in the X-ray and radio bands than the majority of BL Lacs found at much lower redshifts. If WLQs are high-redshift BL Lacs, then it is difficult to explain the lack of a large parent population of X-ray and radio bright weak-lined sources at high redshift. We also consider the possibility that WLQs are quasars with extreme properties, and in particular that the emission lines are suppressed by high accretion rates. Using joint spectral fitting of the X-ray spectra of 11 WLQs we find that the mean photon index in the hard X-ray band is consistent with those observed in typical radio-quiet AGNs with no hint of an unusually steep hard-X-ray spectrum. This result poses a challenge to the hypothesis that WLQs have extremely high accretion rates, and we discuss additional observations required to test this idea.
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