It is shown that electron-phonon interaction provides a natural explanation for the unusual band dispersion of the metallic surface states at the Si(111)-(7 x 7) surface. Angle-resolved photoemission reveals a discontinuity of the adatom band at a binding energy close to the dominant surface phonon mode at h(omega0) = 70 meV. This mode has been assigned to adatom vibrations by molecular dynamics calculations. A calculation of the spectral function for electron-phonon interaction with this well-defined Einstein mode matches the data. Two independent determinations of the electron-phonon coupling parameter from the band dispersion and from the temperature-dependent phonon broadening yield similar values of lambda = 1.09 and lambda = 1.06.