The dipole response in neutron rich nuclei is investigated within self-consistent approaches which make direct use of a nucleon-nucleon optimized chiral potential complemented with a density dependent term simulating a three-body force. Hartree-Fock-Bogoliubov plus Tamm-Dancoff and random-phase approximations show that such a potential improves the description of the dipole modes with respect to other realistic interactions. The inclusion of the two-phonon states within an equation of motion method induces a pronounced fragmentation of both giant and pygmy resonances in agreement with recent experiments.