  We report the first high-resolution X-ray spectra of two high-redshift
quasars, S5 0836+710 and PKS 2149-306, obtained with the Chandra High Energy
Transmission Grating Spectrometer (HETGS). The primary goal of this observation
is to use the high spectral resolving power of the HETGS to detect X-ray
absorption produced by a hot intergalactic medium. The continuum of both
quasars can be fitted by absorbed power laws. The power law photon index
(Gamma) of S5 0836+710 is consistent with that found in previous observations
with ROSAT and ASCA, while the power law of PKS 2149-306 is harder than found
in a previous observation by ASCA. Excess continuum absorption above the
Galactic value is found in S5 0836+710, as evidenced in ASCA and ROSAT
observations. No significant emission or absorption feature is detected in
either source at 3 sigma level. Based on the detection limits we constrain the
properties of possible emitters and absorbers. The upper limit of the
equivalent width of Fe K emission lines could be as low as ~ 10 eV. Absorbers
with a column density higher than 8e16 cm^{-2} for O VIII or 5e16 cm^{-2} for
Si XIV would have been detected. We propose a method to constrain the
cosmological parameters (namely Omega_0 and Omega_b) via the X-ray forest
theory, but current data do not give significant constraints. However, we
estimate that observing ~ 7 bright quasars should give at least one O VIII and
more O VII absorption lines at 95% possibility. We also find that combined with
the constraints from the distortion of the CMB spectrum, the X-ray
Gunn-Peterson test can marginally constrain a uniform, enriched IGM.
