Phase separation of liquid mixtures into two liquids with different compositions is a well-known phenomenon. It has been proposed(1-9) that another type of liquid-liquid phase separation, driven by fluctuations in density rather than in composition, may occur in some elemental systems. Transitions between low- and high-density amorphous phases have been described for the one-component oxides H2O, SiO2 and GeO2 (refs 10-17), and it has been suggested(18-21) that a liquid-liquid phase transition might occur in supercooled water. If density-driven phase separation truly does occur in liquid mixtures, it should be possible to observe the coexistence of two liquids with the same composition but different density. Here we report the direct observation of such a situation. We observe two coexisting liquid phases in the supercooled melt of Al2O3-Y2O3 just above the glass transition at ambient pressure, both of which have the same composition. We propose that these two phases must differ solely in density, and that the transition is entropically driven. The occurrence of the phase transition in this system may explain why the crystallization of yttrium aluminium garnet, the host material for Nd3+ ions in YAG lasers, is sluggish(22-25).