  In this paper we calculate the electron-phonon coupling of the
newly-discovered superconductor LaO$_{1-x}$F$_x$FeAs from first-principles,
using Density Functional Perturbation Theory. For pure LaOFeAs, the calculated
electron-phonon coupling constant $\lambda=0.21$ and logarithmic-averaged
frequency $\omega_{ln}=206 K$, give a maximum $T_c$ of 0.8 K, using the
standard Migdal-Eliashberg theory.
  For the $F-$doped compounds, we predict even smaller coupling constants, due
to the strong suppression of the electronic Density of States at the Fermi
level. To reproduce the experimental $T_c=26 K$, 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 newly-discovered LaO$_{1-x}$F$_x$FeAs
superconductor, probably due to the importance of strong correlation effects.
