AbstractRecent findings of structural glasses with extremely high kinetic and thermodynamic stability have attracted much attention. The question has been raised as to whether the well-known, low-temperature “glassy anomalies” (attributed to the presence of two-level systems [TLS] and the “boson peak”) persist or not in these ultrastable glasses of much lower configurational entropy. To resolve previous contradictory results, we study a particular type of ultrastable glass, TPD, which can be prepared by physical vapor deposition in a highly-stable state with different degrees of layering and molecular orientation, and also as a conventional glass and in crystalline state. After a thorough characterization of the different samples prepared, we have measured their specific heat down to 0.4 K. Whereas the conventional glass exhibits the typical glassy behaviour and the crystal the expected Debye cubic dependence at very low temperatures, a strong depletion of the TLS contribution is found in both kinds of ultrastable glass, regardless of their layering and molecular ordering.