By converting the energy of nuclear radiation to excited electrons and holes, semiconductor detectors have provided a highly efficient way for detecting them, such as photons or charged particles. However, for detecting the radiated neutrons, those conventional semiconductors hardly behave well, as few of them possess enough capability for capturing these neutral particles. While the element Gd has the highest nuclear cross section, here for searching proper neutron-detecting semiconductors, we investigate theoretically the Gd chalcogenides whose electronic band structures have never been characterized clearly. Among them, we identify that γ-phase Gd2Se3 should be the best candidate for neutron detecting since it possesses not only the right bandgap of 1.76 eV for devices working under room temperature but also the desired indirect gap nature for charge carriers surviving longer. We propose further that semiconductor neutron detectors with single-neutron sensitivity can be realized with such a Gd-chalcogenide on the condition that their crystals can be grown with good quality.