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Using density functional theory calculations we establish the hithertounknown compound CrCTe$_3$ to be a stable anti-ferromagnetic semiconductor inthe R$\bar{3}$ crystal structure with an indirect fundamental gap . Successivelayers in the bulk compound are weakly bound by van der Waals forces so thatindividual layers can be easily exfoliated. A monolayer of CrCTe$_3$ is also ananti-ferromagnetic semiconductor. The monolayer is structurally stable over alarge range of compressive and tensile strains, and the anti-ferromagneticstate is robust over this strain range. Band gap of the monolayer can be tunedby as much as 50% by applying strain in this range.

CrCTe$_3$: Computational design of a robust two-dimensional anti-ferromagnetic semiconductor