  Ionizing sources embedded in the neutral intergalactic medium (IGM) before
cosmological reionization generate discrete HII regions. We show that a
sufficiently bright quasar (for example, one tenth as luminous as that recently
discovered by Fan et al.) can ionize a large volume, allowing the transmission
of a substantial fraction of the flux of its intrinsic Lyman alpha emission
line on both sides of the Lyman alpha wavelength. The observed line profile is
richly informative. We show that a sufficiently accurate, high spectral
resolution ($R\approx 10^4$) measurement of the line profile of a bright quasar
is feasible using the Next Generation Space Telescope (NGST) as well as large
ground-based telescopes. Such a measurement has two potentially important
applications. First, the red side of the Lyman alpha emission line provides a
way to measure the quasar lifetime. Second, the blue side provides a direct
measure of the density fluctuations of the intergalactic medium at the quasar
redshift. The estimate of the absorption of the red side is limited by the
accuracy to which the intrinsic profile of the Lyman alpha emission line is
known. The blue side, however, does not sensitively depend on the intrinsic
profile, because the former is much narrower than the latter.
