We report findings from the first set of data in a current survey to establish conclusively whether jets from young stars rotate. We observed the bipolar jets from the T Tauri stars TH 28 and RW Aur and the blueshifted jet from T Tauri star LkHα 321, using the Hubble Space Telescope Imaging Spectrograph. Forbidden emission lines show distinct and systematic velocity asymmetries of 10-25 (±5) km s^-1 at a distance of 03 from the source, representing a (projected) distance of ≈40 AU along the jet in the case of RW Aur, ≈50 AU for TH 28, and 165 AU in the case of LkHα 321. These velocity asymmetries are interpreted as rotation in the initial portion of the jet where it is accelerated and collimated. For the bipolar jets, both lobes appear to rotate in the same direction. Values obtained were in agreement with the predictions of MHD disk-wind models. Finally, we determine, from derived toroidal and poloidal velocities, values for the distance from the central axis of the footpoint for the jet's low-velocity component of ≈0.5-2 AU, consistent with the models of magnetocentrifugal launching.