Current compilations of previously documented inorganic compounds reveal a significant number of materials that are not listed. Focusing on the A2BX4 metal-chalcogenide group with A and B atoms being either main group elements or only one of them being a 3d transition metal, a total of 255 are reported, whereas 429 are unreported. We have applied first-principles thermodynamics based on density functional methodology, predicting that about 100 of the 429 unreported A2BX4 metal-chalcogenides are likely to be stable. These include 14 oxides, 34 sulfides, 28 selenides and 24 tellurides, that are predicted here to be energetically stable with respect to decomposition into any combination of elemental, binary, and ternary competing phases. We provide the predicted lowest-energy crystal structures of the predicted A2BX4 compounds, as well as the next few energetically higher metastable structures. Such predictions are carried out via direct first-principles calculations of candidate structure types and confirmed for a few compounds using the global space-group optimization (GSGO) search method. In some cases, uncommon oxidation states and/or coordination environments are found for elements in the new stable A2BX4 compounds. We estimated the growth conditions in terms of temperature and partial pressure of the reactants from extensive thermodynamic stability analysis, and found dozens of new compounds that might be grown at normal synthesis conditions. Attempts at synthesis of the new stable A2BX4 compounds predicted here are called for.