Topological insulators (TIs) have been found in strained binary HgTe and ternary I-III-VI 2 chalcopyrite compounds such as CuTlSe 2 which have inverted band structures. However, the nontrivial band gaps of these existing binary and ternary TIs are limited to small values, usually around 10 meV or less. In this work, we reveal that a large non-trivial band gap requires the material having a large negative crystal field splitting ∆ CF at top of the valence band and a moderately large negative s − p band gap E s−p g . These parameters can be better tuned through chemical ordering in multinary compounds. Based on this understanding, we show that a series of quaternary I 2 -II-IV-