  We report the detection of quiescent H_2 emission in the v=1-0 S(1) line at
2.12183 um in the circumstellar environment of two classical T Tauri stars, GG
Tau A and LkCa 15, in high-resolution (R 60,000) spectra, bringing to four,
including TW Hya and the weak-lined T Tauri star DoAr 21, the number of T Tauri
stars showing such emission. The equivalent widths of the H_2 emission line lie
in the range 0.05-0.10 \AA and, in each case, the central velocity of the
emission line is centered at the star's systemic velocity. The line widths
range from 9 to 14 km s^{-1}, in agreement with those expected from gas in
Keplerian orbits in circumstellar disks surrounding K-type stars at distances >
10 AU from the sources. We suggest that UV fluorescence and X-ray heating are
likely candidates responsible for producing the observed emission. We present
mass estimates from the measured line intensities and show that the estimated
masses are consistent with those expected from the possible mechanisms
responsible for stimulating the observed emission. The high temperatures and
low densities required for significant emission in the v=1-0 S(1) line suggests
that we have detected reservoirs of hot H_2 gas located in the low density,
upper atmospheres of circumstellar disks of these stars.
