  The isovector dipole response in $^{208}$Pb is described in the framework of
a fully self-consistent relativistic random phase approximation. The NL3
parameter set for the effective mean-field Lagrangian with nonlinear meson
self-interaction terms, used in the present calculations, reproduces ground
state properties as well as the excitation energies of giant resonances in
nuclei. In addition to the isovector dipole resonance in $^{208}$Pb, the
present analysis predicts the occurrence of low-lying E1 peaks in the energy
region between 7 and 11 MeV. In particular, a collective state has been
identified whose dynamics correspond to that of a dipole pygmy resonance: the
vibration of the excess neutrons against the inert core composed of equal
number of protons and neutrons.
