A small amount of locally reversible melting and crystallization in poly(ethylene terephthalate) (PET) has been detected by temperature-modulated differential scanning calorimetry (TMDSC). Extended-time TMDSC was used in the quasi-isothermal mode. Studied were melt-crystallized, quenched, and a biaxially-oriented film of PET in temperature steps of 2 K from 320 to 560 K. The integral of the endothermic and exothermic latent heat contributions to the reversible melting and crystallization is less than 10% of the total heat of fusion and decreases further with time over many hours. The new observations support the concept that "molecular nucleation" is the reversible and rate-determining step in crystallization. On TMDSC, partially-melted chains remain on the surface of higher-melting crystals to permit crystallization during the cooling cycle without supercooling.