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We predict by first-principles calculations that p-doped graphane is an electron-phonon superconductor with a critical temperature above the boiling point of liquid nitrogen. The unique strength of the chemical bonds between carbon atoms and the large density of electronic states at the Fermi energy arising from the reduced dimensionality give rise to a giant Kohn anomaly in the optical phonon dispersions and push the superconducting critical temperature above 90 K. As evidence of graphane was recently reported, and doping of related materials such as graphene, diamond, and carbon nanostructures is well established, superconducting graphane may be feasible.