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Evolutionary searches predicted a number of ternary phases that could besynthesized at pressures of 100-300~GPa. $P6_3/mmc$ CaSH$_2$, $Pnma$ CaSH$_2$,$Cmc2_1$ CaSH$_6$, and $I\bar{4}$ CaSH$_{20}$ were composed of a Ca-S latticealong with H$_2$ molecules coordinated in a ``side-on'' fashion to Ca. The H-Hbond lengths in these semiconducting phases were elongated because of H$_2$$\sigma\rightarrow$ Ca d donation, and Ca d$\rightarrow$ H$_2$ $\sigma^*$back-donation, via a Kubas-like mechanism. $P\bar{6}m2$ CaSH$_3$, consisting oftwo-dimensional HS and CaH$_2$ sheets, was metastable and metallic above\edit{128~GPa}. The presence of van Hove singularities increased its density ofstates at the Fermi level, and concomitantly the superconducting criticaltemperature, which was estimated to be as high as \edit{$\sim$100~K at128~GPa}. This work will inspire the search for superconductivity in materialsbased upon \edit{honeycomb HX (X=S, Se, Te), and MH$_2$ (M=Mg, Ca, Sr, Ba)layers} under pressure.

A Metastable CaSH$_3$ Phase Composed of HS Honeycomb Sheets that is Superconducting Under Pressure