We have detected emission from the quiescent, molecular hydrogen gas in the disk around the X-ray bright, classical T Tauri star TW Hya in the 1¨0 S(1) line at 2.1218 km through high-resolution spectros- copy using CSHELL on NASAs Infrared Telescope Facility. The brightness of the observed emission line is consistent with that predicted from models for X-ray excitation of the 1¨0 S(1) line of This H 2 . result demonstrates that X-ray ionization is a plausible mechanism for excitation of the in the H 2 gaseous disks of T Tauri stars. In addition, from these high-resolution spectra we have measured the radial velocities of three T Tauri stars in the TW Hya association, CD (33i7795, HD 98800, and TW Hya. We —nd that the radial velocities of these three stars are very similar to each other and to those of at least three other stars presumed to be members of the TW Hya association, Hen 600A, Hen 600B, and CD (29i8887. This result, combined with the similar proper motions of all six of these stars, lends support to the hypothesis that all of these stars share a common origin in a now-dispersed molecular cloud. Subject headings: infrared: starsopen clusters and associations: individual (TW Hydrae, HD 98800, CD (33i7795) ¨ stars: premain-sequenceX-rays: stars