Expanding the library of known inorganic materials with functional electronic or magnetic behavior is a longstanding goal in condensed matter physics and materials science. Recently, the transition metal chalchogenides including selenium and sulfur have been of interest because of their correlated-electron properties, as seen in the iron based superconductors and the transition metal dichalcogenides. However, the chalcogenide chemical space is less explored than that of oxides, and there is an open question of whether there may be new materials heretofore undiscovered.We perform a systematic combined theoretical and experimental search over ternary phase diagrams that are empty in the Inorganic Crystal Structure Database containing cations, transition metals, and one of selenium or sulfur. In these 27 ternary systems, we use a probabilistic model to reduce the likelihood of false negative predictions, which results in a list of 24 candidate materials.We then conduct a variety of synthesis experiments to check the candidate materials for stability.While the prediction method did obtain previously unknown compositions that are predicted stable within density functional theory, none of the candidate materials formed in our experiments. We come to the conclusion that these phase diagrams are "empty" in the case of bulk synthesis, but it remains a possibility that alternate synthesis routes may produce some of these phases.