We investigate a lattice version of QED by numerical simulations. For the renormalized charge and mass we find results which are consistent with the renormalized charge vanishing in the continuum limit. A detailed study of the relation between bare and renormalized quantities reveals that the Landau pole lies in a region of parameter space which is made inaccessible by spontaneous chiral symmetry breaking. (orig.)10 refs.SIGLEAvailable from TIB Hannover: RA 2999(97-252) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman