  We report local probe ($\mu$SR) measurements on the recently discovered
tetragonal FeS superconductor which has been predicted to be electronically
very similar to superconducting FeSe. Most remarkably, we find that low moment
($10^{-2}-10^{-3}\mu_\mathrm{B})$ disordered magnetism with a transition
temperature of $T_\mathrm{N}\approx 20$ K microscopically coexists with bulk
superconductivity below $T_\mathrm{c}=4.3(1)$ K. From transverse field $\mu$SR
we obtain an in-plane penetration depth $\lambda_\mathrm{ab}(0)=223(2)$ nm for
FeS. The temperature dependence of the corresponding superfluid density
$\lambda_\mathrm{ab}^{-2}(T)$ indicates a fully gapped superconducting state
and is consistent with a two gap s-wave model. Additionally, we find that the
superconducting $T_\mathrm{c}$ of FeS continuously decreases for hydrostatic
pressures up to 2.2 GPa.
