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The knowledge of the existence of liquid water under extreme conditions and its concomitant properties are important in many fields of science. Glassy water has previously been prepared by hyperquenching micron-sized droplets of liquid water and vapor deposition on a cold substrate (ASW), and its transformation to an ultraviscous liquid form has been reported on heating. A densified amorphous solid form of water, high-density amorphous ice (HDA), has also been made by collapsing the structure of ice at pressures above 1 GPa and temperatures below approximately 140 K, but a corresponding liquid phase has not been detected. Here we report results of heat capacity C(p) and thermal conductivity, in situ, measurements, which are consistent with a reversible transition from annealed HDA to ultraviscous high-density liquid water at 1 GPa and 140 K. On heating of HDA, the C_p increases abruptly by (3.4 ± 0.2) J mol^-1 K^-1 before crystallization starts at (153 ± 1) K. This is larger than the C_p rise at the glass to liquid transition of annealed ASW at 1 atm, which suggests the existence of liquid water under these extreme conditions.