  Recent developments in numerical relativity have made it possible to follow
reliably the coalescence of two black holes from near the innermost stable
circular orbit to final ringdown. This opens up a wide variety of exciting
astrophysical applications of these simulations. Chief among these is the net
kick received when two unequal mass or spinning black holes merge. The
magnitude of this kick has bearing on the production and growth of supermassive
black holes during the epoch of structure formation, and on the retention of
black holes in stellar clusters. Here we report the first accurate numerical
calculation of this kick, for two nonspinning black holes in a 1.5:1 mass
ratio, which is expected based on analytic considerations to give a significant
fraction of the maximum possible recoil. We have performed multiple runs with
different initial separations, orbital angular momenta, resolutions, extraction
radii, and gauges. The full range of our kick speeds is 86--116 km s$^{-1}$,
and the most reliable runs give kicks between 86 and 97 km s$^{-1}$. This is
intermediate between the estimates from two recent post-Newtonian analyses and
suggests that at redshifts $z\gtrsim 10$, halos with masses $\lesssim 10^9
M_\odot$ will have difficulty retaining coalesced black holes after major
mergers.
