Highly porous carbide-derived carbon fibers have been synthesized by electrospinning of polycarbosilane with subsequent pyrolysis and chlorination. The resulting ultrathin fibers show specific surface areas up to 3116 m² g^-1 and very high storage capacities for hydrogen up to 3.86 wt.% at 17 bar and 77 K. Due to the outstanding adsorption performance and other properties such as high temperature stability and the unique CDC fiber shape, this new kind of fiber material offers promising possibilities for several applications like air or liquid filters or textiles for protective clothing. Application as a flexible electrode material for supercapacitors is conceivable.