Electronic structure calculations from first principles are employed to design half-metallic fully compensated ferrimagnets (or, as they are widely known, half-metallic antiferromagnets) susceptible of finding applications in spintronics. Cr(2)MnZ (Z=P,As,Sb,Bi) compounds have 24 valence electrons per unit cell and calculations show that their total spin moment is approximately zero for a wide range of lattice constants, in agreement with the Slater-Pauling behavior for ideal half-metals. Simultaneously, the spin magnetic moments of Cr and Mn atoms are antiparallel and the compounds are ferrimagnets. Mean-field approximation is employed to estimate their Curie temperature, which exceeds room temperature for the alloy with Sb. Our findings suggest that Cr2MnSb is the compound of choice for further experimental investigations.