  In this work we evaluate the $^1S_0$ energy gap of $\Sigma^-$ hyperons in
$\beta$-stable neutron star matter. We solve the BCS gap equation for an
effective $\Sigma^-\Sigma^-$ pairing interaction derived from the most recent
parametrization of the hyperon-hyperon interaction constructed by the Nijmegen
group. We find that the $\Sigma^-$ hyperons are in a $^1S_0$ superfluid state
in the density region $\sim 0.27-0.7$ fm$^{-3}$, with a maximum energy gap of
order 8 MeV at a total baryon number density of $\sim 0.37$ fm$^{-3}$ and a
$\Sigma^-$ fraction of about 8%. We examine the implications on neutron star
cooling.
