A melt has greater volume than a silicate solid of the same composition. But this difference diminishes at high pressure, and the possibility that a melt sufficiently enriched in the heavy element iron might then become more dense than solids at the pressures in the interior of the Earth (and other terrestrial bodies) has long been a source of considerable speculation(1,2). The occurrence of such dense silicate melts in the Earth's lowermost mantle would carry important consequences for its physical and chemical evolution and could provide a unifying model for explaining a variety of observed features in the core-mantle boundary region(3). Recent theoretical calculations(4) combined with estimates of iron partitioning between (Mg,Fe)SiO(3) perovskite and melt at shallower mantle conditions(5-7) suggest that melt is more dense than solids at pressures in the Earth's deepest mantle, consistent with analysis of shockwave experiments(8). Here we extend measurements of iron partitioning over the entire mantle pressure range, and find a precipitous change at pressures greater than similar to 76 GPa, resulting in strong iron enrichment in melts. Additional X-ray emission spectroscopy measurements on (Mg(0.95)Fe(0.05))SiO(3) glass indicate a spin collapse around 70 GPa, suggesting that the observed change in iron partitioning could be explained by a spin crossover of iron (from high-spin to low-spin) in silicate melt. These results imply that (Mg,Fe)SiO(3) liquid becomes more dense than coexisting solid at similar to 1,800 km depth in the lower mantle. Soon after the Earth's formation, the heat dissipated by accretion and internal differentiation could have produced a dense melt layer up to similar to 1,000 km in thickness underneath the solid mantle. We also infer that (Mg,Fe)SiO(3) perovskite is on the liquidus at deep mantle conditions, and predict that fractional crystallization of dense magma would have evolved towards an iron-rich and silicon-poor composition, consistent with seismic inferences of structures in the core-mantle boundary region.