Using density functional theory, we demonstrate that superconductivity in C6Ca is phonon mediated with lambda = 0.83 and phonon frequency (omega)log = 24.7 meV. The calculated isotope exponents are alpha(Ca) = 0.24 and alpha(C) = 0.26. Superconductivity is due mostly to C vibrations perpendicular and Ca vibrations parallel to the graphite layers. Since the electron-phonon couplings of these modes are activated by the presence of an intercalant Fermi surface, the occurrence of superconductivity in graphite intercalated compounds requires a noncomplete ionization of the intercalant.