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 LkHα 264 and the debris disk 49 Cet, and searched for υ = 1− 0S (1) H 2 emission at 2.1218 µm, υ = 1− 0S (0) H 2 emission at 2.2233 µ ma ndυ = 2− 1S (1) H2 emission at 2.2477 µm. The H2 line at 2.1218 µm is detected in LkHα 264 confirming the previous observations by Itoh et al. (2003). In addition, our CRIRES spectra reveal the previously observed but not detected H2 line at 2.2233 µ mi n LkHα 264. An upper limit of 5.3 ×10 −16 erg s −1 cm −2 on the υ = 2− 1S (1) H 2 line flux in LkHα 264 is derived. The detected lines coincide with the rest velocity of LkHα 264. They have a FWHM of ∼20 km s −1 . This is strongly suggestive of a disk origin for the lines. These observations are the first simultaneous detection of υ = 1− 0S (1) andυ = 1− 0S (0) H 2 emission from a protoplanetary disk. 49 Cet does not exhibit H2 emission in any of the three observed lines. We derive the mass of optically thin H2 at T ∼ 1500 K in the inner disk of LkHα 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 H2 in the inner disk (∼0.1 AU) of LkHα 264, and less than a tenth of a lunar mass of hot H2 in the inner disk of 49 Cet. The measured 1− 0S (0)/1− 0S (1) and 2− 1S (1)/1−0 S(1) line ratios in LkHα 264 indicate that the H2 emitting gas is at a temperature lower than 1500 K and that the H2 is most likely thermally excited by UV photons. The υ = 1− 0S (1) H 2 line in LkHα 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 ◦ ) and that the line is emitted within a few AU of the LkHα 264 disk. A comparative analysis of the physical properties of classical T Tauri stars in which the H2 υ = 1−0 S(1) line has been detected and non-detected indicates that the presence of H2 emission is correlated with the magnitude of the UV excess and the strength of the Hα line. The lack of H2 emission in the NIR spectra of 49 Cet and the absence of Hα 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.