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This research work is devoted to the problem of ferromagnetism and half-metallicity in systems containing an element of the transition metal family, chromium. In fact, 3d electron-based magnetism in transition metals has been experimentally observed and/or theoretically predicted to exist in a large number of materials. To this end, this study is a theoretical investigation based on ab-initio calculations for the exploration of half-metallicity in binary materials of the Cr-X family based on group VI elements (X=S, Se and Te), in five different crystal structures, three cubic structures, NaCl, CsCl and zinc-blende (ZB), and two hexagonal structures, wurtzite (WZ), and NiAs. For our calculations, we have chosen to work within the framework of density functional theory (DFT), using two types of approximation, GGA-PBEsol and mBJ GGA-PBEsol.