  The supermassive black hole at the center of a distant galaxy can be weighed,
in rare but realistic cases, when the galaxy acts as a strong gravitational
lens. The central image that should be produced by the lens is either destroyed
or accompanied by a second central image, depending on the mass of the black
hole. We demonstrate that when a central image pair is detected, the mass of
the black hole can be determined with an accuracy of < 0.1 dex, if the form of
the smooth mass distribution near the galaxy core is known. Uncertainty in the
central mass distribution introduces a systematic error in the black hole mass
measurement. However, even with nearly complete ignorance of the inner mass
distribution, the black hole mass can still be determined to within a factor of
10. Central image pairs should be readily observable with future radio
interferometers, allowing this technique to be used for a census of
supermassive black holes in inactive galaxies at significant redshift (0.2 < z
< 1.0).
