The melting curve of FeSi has been determined to 150 GPa in the laser-heated diamond anvil cell (LH-DAC) on the basis of discontinuities in the power versus temperature function. A multianvil experimental cross-check at 12 GPa using textural criteria as a proxy for melting is in good agreement with our LH-DAC results. The melting point of FeSi reaches ∼4000 K at the core mantle boundary and an extrapolated value of 4900 K at the inner-core boundary (ICB). We also present the melting curve as determined by the Lindemann melting law; this agrees well with our experimental curve to 70 GPa and then diverges to higher temperatures, reaching 6200 K at the ICB. These temperatures are substantially higher than previous LH-DAC determinations. The boundary of the ε-FeSi → CsCl-FeSi subsolidus transition has also been determined by synchrotron-based X-ray diffraction at high pressures, and the results confirm a negative Clapeyron slope for the transition. We conclude that if present, FeSi is likely to be solid within the D″ layer and is unlikely to be present within the inner core for any plausible bulk core silicon content.