  We calculate the kick generated by an eccentric black hole binary inspiral as
it evolves through a resonant orbital configuration where the precession of the
system temporarily halts. As a result, the effects of the asymmetric emission
of gravitational waves build up coherently over a large number of orbits. Our
results are calculate using black hole perturbation theory in the limit where
the ratio of the masses of the orbiting objects $\epsilon=m/M$ is small. The
resulting kick velocity scales as $\epsilon^{3/2}$, much faster than the
$\epsilon^2$ scaling of the kick generated by the final merger. For the most
extreme case of a very eccentric ($e\sim 1$) inspiral around a maximally
spinning black hole, we find kicks close to $30,000\;\epsilon^{3/2}$~km/s,
enough to dislodge a black hole from its host cluster or even galaxy. In
reality, such extreme inspirals should be very rare. Nonetheless, the
astrophysical impact of kicks in less extreme inspirals could be
astrophysically significant.
