Four three-phase coexisting curves for the trifluoromethane hydrate system were obtained over a pressure range up to 72 MPa and temperature range from 283 to 302 K. Two invariant points determined in the present study are the critical end point of 299.44 K and 4.85 MPa, and the quadruple point of 292.25 K and 4.07 MPa. The former, where the gas and liquid are critically identical in the presence of water phase, is located very close to the critical point of the trifluoromethane fluid. The latter is the terminal point of four three-phase coexisting curves. The overall enthalpy change of hydration is estimated over the whole temperature region. The important finding is that trifluoromethane hydrate is the border system having a quadruple point (hydrate + two liquids + gas) in a series of critical temperatures of known guest species. It is also identified that xenon hydrate is the opposite border system having no quadruple point.