In situ transmission electron microscopy reveals that an atomically thin crystalline phase at the surface of liquid Au-Si is stable over an unexpectedly wide range of conditions. By measuring the surface structure as a function of liquid temperature and composition, a simple thermodynamic model is developed to explain the stability of the ordered phase. The presence of surface ordering plays a key role in the pathway by which the Au-Si eutectic solidifies and also dramatically affects the catalytic properties of the liquid, explaining the anomalously slow growth kinetics of Si nanowires at low temperature. A strategy to control the presence of the surface phase is discussed, using it as a tool in designing strategies for nanostructure growth.