Despite a plethora of materials suggested for spintronic applications, a new class of materials has emerged, namely spin gapless semiconductors (SGS), which offers potentially more advantageous properties than existing ones. These magnetic semiconductors exhibit a finite band gap for one spin channel and a closed gap for the other. Here, supported by electronic-structure calculations, we report evidence of SGS behavior in equiatomic quaternary CoFeCrGa, having a cubic Heusler (prototype LiMgPdSn) structure but exhibiting chemical disorder (DO3 structure). CoFeCrGa is found to transform from SGS to half-metallic phase under pressure, which is attributed to unique electronic-structure features. The saturation magnetization (MS) obtained at 8K agrees with the Slater-Pauling rule and the Curie temperature (TC) is found to exceed 400K. Carrier concentration (up to 250K) and electrical conductivity are observed to be nearly temperature independent, prerequisites for SGS. The anomalous Hall coefficient is estimated to be 185S/cm at 5K. Considering the SGS properties and high TC, this material appears to be promising for spintronic applications.