  We report the discovery of quiescent emission from molecular hydrogen gas
located in the circumstellar disks of six pre-main sequence stars, including
two weak-line T Tauri stars (TTS), and one Herbig AeBe star, in the Chamaeleon
I star forming region. For two of these stars, we also place upper limits on
the 2->1 S(1)/1->0 S(1) line ratios of 0.4 and 0.5. Of the 11 pre-main sequence
sources now known to be sources of quiescent near-infrared hydrogen emission,
four possess transitional disks, which suggests that detectable levels of H$_2$
emission and the presence of inner disk holes are correlated. These H$_2$
detections demonstrate that these inner holes are not completely devoid of gas,
in agreement with the presence of observable accretion signatures for all four
of these stars and the recent detections of [Ne II] emission from three of
them. The overlap in [Ne II] and H$_2$ detections hints at a possible
correlation between these two features and suggests a shared excitation
mechanism of high energy photons. Our models, combined with the kinematic
information from the H$_2$ lines, locate the bulk of the emitting gas at a few
tens of AU from the stars. We also find a correlation between H$_2$ detections
and those targets which possess the largest H$\alpha$ equivalent widths,
suggesting a link between accretion activity and quiescent H$_2$ emission. We
conclude that quiescent H$_2$ emission from relatively hot gas within the disks
of TTS is most likely related to on-going accretion activity, the production of
UV photons and/or X-rays, and the evolutionary status of the dust grain
populations in the inner disks.
