We observed 17 optically-selected, radio-quiet high-redshift quasars with the Chandra Observatory ACIS, and detected 16 of them. The quasars have redshift between 3.70 and 6.28 and include the highest redshift quasars known. When compared to low-redshift quasars observed with ROSAT, these high redshift quasars are significantly more X-ray quiet. We also find that the X-ray spectral index of the high redshift objects is flatter than the average at lower redshift. These trends confirm the predictions of models where the accretion flow is described by a cold, optically-thick accretion disk surrounded by a hot, optically thin corona, provided the viscosity parameter alpha >= 0.02. The high redshift quasars have supermassive black holes with masses ~10^{10} M_{sun}, and are accreting material at ~0.1 the Eddington limit. We detect 10 X-ray photons from the z=6.28 quasar SDS 1030+0524, which may have a Gunn-Peterson trough and be near the redshift of reionization of the intergalactic medium. The X-ray data place an upper limit on the optical depth of the intergalactic medium tau(IGM) < 10^6, compared to the lower limit from the spectrum of Lyalpha and Lybeta, which implies tau(IGM) > 20.
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