Twenty-one orbits of Lunar Prospector magnetometer data obtained during an extended passage of the Moon through a lobe of the geomagnetic tail in April 1998 are applied to estimate the residual lunar induced magnetic dipole moment. Editing and averaging of individual orbit segments yields a negative induced moment with amplitude -2.4¿1.6¿1022 Gauss-cm3 per Gauss of applied field. Assuming that the induced field is caused entirely by electrical currents near the surface of a highly electrically conducting metallic core, the preferred core radius is 340¿90 km. For an iron-rich composition, such a core would represent 1 to 3% of the lunar mass. ¿ 1999 American Geophysical Union