  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.
