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We report results of a computational work on the half-Heusler compound CrMnSb_(1-x)P_x. We show that the parent compound CrMnSb is nearly half-metallic, with the onset of the band gap a few meV above the Fermi energy. Moreover, although it undergoes a half-metallic transition under a uniform compression of ~1.5%, such transition is absent under epitaxial strain. The half-metallic transition could be induced by a chemical substitution of Sb with P, which results in a volume reduction of the unit cell. In particular, 50% substitution of Sb with P leads to a robust half-metallicity, with 100% spin polarization being retained at a large range of epitaxial strain. Thus, our results indicate that CrMnSb_0.5P_0.5 could be grown on different types of substrates, e.g. GaAs, without its electronic properties being detrimentally affected by biaxial strain. In addition, CrMnSb_0.5P_0.5 exhibits a fully compensated ferrimagnetic alignment, which could be potentially useful in applications where stray magnetic fields are undesirable.