  In this work we calculate the $^1S_0$ gap energies of $\Lambda$ hyperons in
neutron star matter. The calculation is based on a solution of the BCS gap
equation for an effective G-matrix parameterization of the $\Lambda-\Lambda$
interaction with a nuclear matter background, presented recently by Lanskoy and
Yamamoto. We find that a gap energy of a few tenths of MeV is expected for
$\Lambda$ Fermi momenta up to about 1.3 fm$^{-1}$. Implications for neutron
star matter are examined, and suggest the existence of a $\Lambda$ $^1S_0$
superfluid between the threshold baryon density for $\Lambda$ formation and the
baryon density where the $\Lambda$ fraction reaches $15-20%$.
