We introduce a method to fabricate high-performance field-effect transistors on the surface of freestanding organic single crystals. The transistors are constructed by laminating a monolithic elastomeric transistor stamp against the surface of a crystal. This method, which eliminates exposure of the fragile organic surface to the hazards of conventional processing, enables fabrication of rubrene transistors with charge carrier mobilities as high as approximately 15 cm2/V.s and subthreshold slopes as low as 2nF.V/decade.cm2. Multiple relamination of the transistor stamp against the same crystal does not affect the transistor characteristics; we exploit this reversibility to reveal anisotropic charge transport at the basal plane of rubrene.