Recent experiments showed that some layered ternary transition metal trichalcogenide compounds are efficient catalysts for the hydrogen evolution reaction (HER). Motivated by these, we have combinatorially designed and computationally screened, through an efficient, automated approach based on density functional theory, single layers of such compounds, including those not reported in widely used crystal structure database like the International Crystal Structure Database (ICSD), for their efficiency as HER catalysts. On the basis of our theoretical prediction of overpotentials determined from the reaction coordinate mapping corresponding to the HER mechanism, 13 of these compounds are found to be promising catalysts, out of which three are suggested to be as efficient as platinum, the best known HER catalyst to date.