Molybdenum sulfides are very attractive noble-metal-free electrocatalysts for the hydrogen evolution reaction (HER) from water. The atomic structure and identity of the catalytically active sites have been well established for crystalline molybdenum disulfide (c-MoS2) but not for amorphous molybdenum sulfide (a-MoSx), which exhibits significantly higher HER activity compared to its crystalline counterpart. Here we show that HER-active a-MoSx, prepared either as nanoparticles or as films, is a molecular-based coordination polymer consisting of discrete [Mo3S13](2-) building blocks. Of the three terminal disulfide (S2(2-)) ligands within these clusters, two are shared to form the polymer chain. The third one remains free and generates molybdenum hydride moieties as the active site under H2 evolution conditions. Such a molecular structure therefore provides a basis for revisiting the mechanism of a-MoSx catalytic activity, as well as explaining some of its special properties such as reductive activation and corrosion. Our findings open up new avenues for the rational optimization of this HER electrocatalyst as an alternative to platinum.