The structure of thin-film water on a BaF(2)(111) surface under ambient conditions was studied using x-ray absorption spectroscopy from ambient to supercooled temperatures at relative humidity up to 95%. No hexagonal ice-like structure was observed in spite of the expected templating effect of the lattice-matched (111) surface. The oxygen K-edge x-ray absorption spectrum of liquid thin-film water on BaF(2) exhibits, at all temperatures, a strong resemblance to that of high-density phases for which the observed spectroscopic features correlate linearly with the density. Surprisingly, the highly compressed, high-density thin-film liquid water is found to be stable from ambient (300 K) to supercooled (259 K) temperatures, although a lower-density liquid would be expected at supercooled conditions. Molecular dynamics simulations indicate that the first layer water on BaF(2)(111) is indeed in a unique local structure that resembles high-density water, with a strongly collapsed second coordination shell.