Using well calibrated DFT studies we predict that experimentally synthesized B24 N24 fullerene can serve as a potential reversible chemical hydrogen storage material with hydrogen-gas storage capacity up to 5.13 wt %. Our theoretical studies show that hydrogenation and dehydrogenation of the fullerene framework can be achieved at reasonable rates using existing metal-free hydrogenating agents and base metal-containing dehydrogenation catalysts.