New shock wave equation of state (EOS) data for enstatite and MgSiO3 glass constrain the density change upon melting of Mg-silicate perovskite up to 200 GPa. The melt becomes denser than perovskite near the base of Earth's lower mantle. This inference is confirmed by shock temperature data suggesting a negative pressure-temperature slope along the melting curve at high pressure. Although melting of Earth's mantle involves multiple phases and chemical components, this implies that the partial melts invoked to explain anomalous seismic velocities in the lowermost mantle may be dynamically stable.