We report on the first results of a search for molecular hydrogen emission from protoplanetary disks using CRIRES , ESO ’ s new VLT Adaptive Optics high resolution near-infrared spectrograph . We observed the classical T Tauri star LkH \alpha 264 and the debris disk 49 Cet , and searched for \upsilon = 1 - 0 S ( 1 ) H _ { 2 } emission at 2.1218 \mu m , \upsilon = 1 - 0 S ( 0 ) H _ { 2 } emission at 2.2233 \mu m and \upsilon = 2 - 1 S ( 1 ) H _ { 2 } emission at 2.2477 \mu m. The H _ { 2 } line at 2.1218 \mu m is detected in LkH \alpha 264 confirming the previous observations by Itoh et al . ( 2003 ) . In addition , our CRIRES spectra reveal the previously observed but not detected H _ { 2 } line at 2.2233 \mu m in LkH \alpha 264 . An upper limit of 5.3 \times 10 ^ { -16 } ergs s ^ { -1 } cm ^ { -2 } on the \upsilon = 2 - 1 S ( 1 ) H _ { 2 } line flux in LkH \alpha 264 is derived . The detected lines coincide with the rest velocity of LkH \alpha 264 . They have a FWHM of \sim 20 km s ^ { -1 } . This is strongly suggestive of a disk origin for the lines . These observations are the first simultaneous detection of \upsilon = 1 - 0 S ( 1 ) and \upsilon = 1 - 0 S ( 0 ) H _ { 2 } emission from a protoplanetary disk . 49 Cet does not exhibit H _ { 2 } emission in any of the three observed lines . We derive the mass of optically thin H _ { 2 } at T \sim 1500 K in the inner disk of LkH \alpha 264 and derive stringent limits in the case of 49 Cet at the same temperature . There are a few lunar masses of optically thin hot H _ { 2 } in the inner disk ( \sim 0.1 AU ) of LkH \alpha 264 , and less than a tenth of a lunar mass of hot H _ { 2 } in the inner disk of 49 Cet . The measured 1-0 S ( 0 ) /1-0 S ( 1 ) and 2-1 S ( 1 ) /1-0 S ( 1 ) line ratios in LkH \alpha 264 indicate that the H _ { 2 } emitting gas is at a temperature lower than 1500 K and that the H _ { 2 } is most likely thermally excited by UV photons . The \upsilon = 1 - 0 S ( 1 ) H _ { 2 } line in LkH \alpha 264 is single peaked and spatially unresolved . Modeling of the shape of the line suggests that the disk should be seen close to face-on ( i < 35 ^ { o } ) and that the line is emitted within a few AU of the LkH \alpha 264 disk . A comparative analysis of the physical properties of classical T Tauri stars in which the H _ { 2 } \upsilon = 1 - 0 S ( 1 ) line has been detected and non-detected indicates that the presence of H _ { 2 } emission is correlated with the magnitude of the UV excess and the strength of the H \alpha line . The lack of H _ { 2 } emission in the NIR spectra of 49 Cet and the absence of H \alpha emission suggest that the gas in the inner disk of 49 Cet has dissipated . These results combined with previous detections of ^ { 12 } CO emission at sub-mm wavelengths indicate that the disk surrounding 49 Cet should have an inner hole . We favor inner disk dissipation by inside-out photoevaporation , or the presence of an unseen low-mass companion as the most likely explanations for the lack of gas in the inner disk of 49 Cet .