Heteroanionic compounds that contain more than one type of anion have many unique and attractive properties, which make them desirable for numerous applications. However, because of challenges in synthesis and the complexity of their phase spaces, heteroanionic compounds are much less explored than more traditional homoanionic (single-anion) compounds. In this work, we perform a systematic screening for synthesizable, stable, heteroanionic oxysulfide, oxyselenide, and oxytelluride compounds ABXO (A and B are metals; X = S, Se, and Te) using high-throughput density functional theory calculations. 129 hitherto unknown ABXO compounds are predicted to be thermodynamically stable, therefore potentially synthesizable, and most of them are semiconductors. The calculated band gaps and other electronic and ionic properties are used to further screen potential compounds with promising applications such as thermoelectrics, transparent conductors, and solid-state electrolytes for Li/Na ion batteries. Our initial study on ABXO oxychalcogenides shows that heteroanionic compounds possess an extremely rich phase space with a variety of interesting properties and with a large number of these compounds still awaiting experimental synthesis.