We use a first-principles rational-design approach to identify a previously unrecognized class of antiferroelectric materials in the Pnma MgSrSi structure type. The MgSrSi structure type can be described in terms of antipolar distortions of the nonpolar P6(3)/mmc ZrBeSi structure type, and we find many members of this structure type are close in energy to the related polar P6(3)mc LiGaGe structure type, which includes many members we predict to be ferroelectric. We highlight known ABC combinations in which this energy difference is comparable to the antiferroelectric-ferroelectric switching barrier of PbZrO(3). We calculate structural parameters and relative energies for all three structure types, both for reported and as-yet hypothetical representatives of this class. Our results provide guidance for the experimental realization and further investigation of high-performance materials suitable for practical applications.