Experimental evidence for high temperature diffusion of hydrogen into the interlayer space of graphite is provided. This process is discussed as a possible method for the rapid production of high-quality, inexpensive graphene in large quantities, which could lead to the widespread application of graphene. It was found that hydrogen cations, dissolved in molten LiCl, can be discharged on cathodically polarized graphite rods, which then intercalate into the graphite structure, leading to the peeling of graphite to produce graphene. The graphene nanosheets produced displayed a single-crystalline structure with a lateral size of several hundred nanometers and a high degree of crystallinity and thermal stability. The method introduced could be scaled up to produce industrial quantities of high-quality graphene.