Nanocalorimetry at ultrafast heating rates is used to investigate the glass transition of nanometer thick films of metastable amorphous solid water grown by vapor deposition in an ultrahigh vacuum environment. Apparent heat capacity curves exhibit characteristic features depending on the deposition temperature. While films grown at T 155 K are completely crystallized, those deposited at 90 K show a relaxation exotherm prior to crystallization. Films grown between 135 and 140 K and subsequently cooled down to 90 K reveal a clear endothermic feature before crystallization, which is compatible with a glass-to-liquid transition. The onset temperature is located at 174 K at a heating rate of 2.4 × 104 Ks and is independent of film thickness in the range of 16-150 nm. Comparison of our data with other calorimetric measurements at various heating rates suggests that water is a strong glass former in the deeply supercooled state. © 2012 American Institute of Physics.