  The innermost stable circular orbit (ISCO) of a test particle around a
Schwarzschild black hole of mass $M$ has (areal) radius $r_{\rm isco}= 6M
G/c^2$. If the particle is endowed with mass $\mu(\ll M)$, it experiences a
gravitational self-force whose conservative piece alters the location of the
ISCO. Here we calculate the resulting shifts $\Delta r_{\rm isco}$ and
$\Delta\Omega_{\rm isco}$ in the ISCO's radius and frequency, at leading order
in the mass ratio $\mu/M$. We obtain, in the Lorenz gauge, $\Delta r_{\rm
isco}=-3.269 (\pm 0.003)\mu G/c^2$ and $\Delta\Omega_{\rm isco}/\Omega_{\rm
isco}=0.4870 (\pm 0.0006) \mu/M$. We discuss the implications of our result
within the context of the extreme-mass-ratio binary inspiral problem.
