In this Letter, we calculate the electron-phonon coupling of the newly discovered superconductor LaFeAsO1xFx using linear response. For pure LaFeAsO, the calculated electron-phonon coupling constant 0:21 and logarithmic-averaged frequency !ln 206 K give a maximum Tc of 0.8 K, using the standard Migdal-Eliashberg theory. For the F-doped compounds, we predict even smaller coupling constants. To reproduce the experimental Tc, a 5–6 times larger coupling constant would be needed. Our results indicate that electron-phonon coupling is not sufficient to explain superconductivity in the whole family of Fe-As-based superconductors, probably due to the importance of strong-correlation effects.