Dynamic mechanical thermal analysis performed on cold-drawn polyethylene terephthalate (PET), cold crystallized (annealed) in the temperature interval 100–140 C, reveals the presence of marginally glassy domains above the annealing temperature T a. This suggests that the thermodynamic force driving crystallization causes the structural arrest of some noncrystalline domains. The latter thus need a temperature higher than T a to completely defreeze. Differential scanning calorimetry supports this point of view. Analogous investigations on unoriented PET, cold crystallized in the same conditions, do not show the same peculiarities; thus, chain orientation is relevant to vitrification. This phenomenology is first cast in the language of thermodynamics by introducing an excess chemical potential δ μ describing the presence of structural constraints in the amorphous domains and the effect of chain orientation. For a …