In spite of their importance in fundamental and applied studies, the preparation of endohedral fullerenes has relied on difficult-to-control physical methods. We report a four-step organic reaction that completely closes a 13-membered ring orifice of an open-cage fullerene. This process can be used to synthesize a fullerene C60 encapsulating molecular hydrogen, which can be isolated as a pure product. This molecular surgical method should make possible the preparation of a series of C60 fullerenes, encapsulating either small atoms or molecules, that are not accessible by conventional physical methods.