The electrical conductivity of a charged layer of graphite is calculated from first principles within a tight-binding framework. The Fermi surface consists of circles around the $P$ points in the Brillouin zone. In the neighborhood of these points we obtain analytical expressions for the electron-phonon coupling ${g}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}}}$. The longitudinal and transverse phonons are shown to give exactly the same average contribution to scattering (contrary to the case of simple metals). In the high-temperature limit we obtain a conductivity (at $T=300$ K) that is about thrice that of copper. The significance of this result with respect to graphite intercalation compounds is discussed.