Investigations of two-dimensional transition-metal chalcogenides (TMCs) have recently revealed interesting physical phenomena, including the quantum spin Hall effect(1,2), valley polarization(3,4) and two-dimensional superconductivity(5), suggesting potential applications for functional devices(6-10). However, of the numerous compounds available, only a handful, such as Mo- and W-based TMCs, have been synthesized, typically via sulfurization(11-15), selenization(16,17) and tellurization(18) of metals and metal compounds. Many TMCs are difficult to produce because of the high melting points of their metal and metal oxide precursors. Molten-salt-assisted methods have been used to produce ceramic powders at relatively low temperature(19) and this approach(20) was recently employed to facilitate the growth of monolayer WS2 and WSe2. Here we demonstrate that molten-salt-assisted chemical vapour deposition can be broadly applied for the synthesis of a wide variety of two-dimensional (atomically thin) TMCs. We synthesized 47 compounds, including 32 binary compounds (based on the transition metals Ti, Zr, Hf, V, Nb, Ta, Mo, W, Re, Pt, Pd and Fe), 13 alloys (including 11 ternary, one quaternary and one quinary), and two heterostructured compounds. We elaborate how the salt decreases the melting point of the reactants and facilitates the formation of intermediate products, increasing the overall reaction rate. Most of the synthesized materials in our library are useful, as supported by evidence of superconductivity in our monolayer NbSe2 and MoTe2 samples(21,22) and of high mobilities in MoS2 and ReS2. Although the quality of some of the materials still requires development, our work opens up opportunities for studying the properties and potential application of a wide variety of two-dimensional TMCs.