  The effect of gravitational radiation reaction on circular orbits around a
spinning (Kerr) black hole is computed to leading order in $S$ (the magnitude
of the spin angular momentum of the hole) and in the strength of gravity $M/r$
(where $M$ is the mass of the black hole, $r$ is the orbital radius, and
$G=c=1$). The radiation reaction makes the orbit shrink but leaves it circular,
and drives the orbital plane very slowly toward antialignment with the spin of
the hole: $\tan (\iota /2) = \tan (\iota_0 /2) [1+(61/72)(S/M^2) (M/r)^{3/2}]$,
where $\iota$ is the angle between the normal to the orbital plane and the spin
direction, and $\iota_0$ is the initial value of $\iota$, when $r$ is very
large.
