We report a shock-tube, laser-schlieren investigation of the molecular dissociation of the title trifluoroethane, CF3CH3 --> CH2CF2 + HF, over very high temperatures, 1600-2400 K, and a wide range of sub-atmospheric pressures, 15-550 Torr. The density gradients are well fit by a simple two-reaction mechanism and accurate dissociation rates obtained. The results are compared with a k(infinity) calculated from a G3 TS for this molecular elimination, which is a superb fit to the available lower-T data and a reliable extrapolation of k(infinity) to high temperatures. The derived rate constants show a very deep falloff from this extrapolation but surprisingly little variation with pressure. This peculiarity is so severe that RRKM calculations dramatically fail to account for the behavior. The dissociation seems to be a clear example of an intrinsic non-RRKM process (nonstatistical dissociation). This conclusion is strongly supported by the observation of double vibrational relaxation at both dissociating and nondissociating temperatures, an unambiguous demonstration of slow IVR. Using a simple model with division into two groups of states, the deep falloff is found to be consistent with a rate-controlling slow IVR, not with low collision efficiency. The model suggests an IVR rate of similar to10(8) s(-1) for dissociation energies.