X-ray diffraction and Raman spectroscopic measurements confirm that molecular hydrogen can be contained within the small water cavities of a binary sH clathrate hydrate using large guest molecules that stabilize the large cavity. The potential increase in hydrogen storage could be more than 40% when compared with binary sII hydrates. This work demonstrates the stabilization of hydrogen in a hydrate structure previously unknown for encapsulating molecular hydrogen, indicating the potential for other inclusion compound materials with even greater hydrogen storage capabilities.