We have designed and built a new apparatus for measuring the thermal conductivity of molten silicates, an adaptation of the transient hot-wire technique to high temperature. The method is the most suitable for high temperatures, as it suppresses convection and minimizes radiative heat transfer. Because of the simple geometry, the radiative transport that does occur can be estimated and subtracted from the total response, yielding true phonic conductivities. Measurements of molten CaMgSi2O6 at approximately 1673, 1773, and 1873 K yield thermal conductivities of 0.31, 0.17 and 0.04 W m-1 K-1 respectively. These values are considerably lower than previous estimates for molten silicates and indicate that the current estimates for the cooling times of magma bodies are probably too short. ¿ American Geophysical Union 1994