  We present a Quantum Monte Carlo study of the zero temperature equation of
state of neutron matter and the computation of the $^1S_0$ pairing gap in the
low-density regime with $\rho<0.04$ fm$^{-3}$. The system is described by a
non-relativistic nuclear Hamiltonian including both two-- and three--nucleon
interactions of the Argonne and Urbana type. This model interaction provides
very accurate results in the calculation of the binding energy of light nuclei.
A suppression of the gap with respect to the pure BCS theory is found, but
sensibly weaker than in other works that attempt to include polarization
effects in an approximate way.
