We study kaonic atoms over the periodic table using a kaon self-energy in the nuclear medium derived from the SU(3) chiral unitary model. This model is quite successful in reproducing the scattering amplitude of meson meson and the strangeness S = − 1 meson baryon reactions. In particular the properties of the Λ ( 1405 ) resonance are well reproduced. In the nuclear medium the properties of this resonance are appreciably modified, and consequently the kaon nucleon scattering amplitudes, leading to an attractive kaon nucleus self-energy for densities higher than ρ 0 / 25. With this interaction we are able to reproduce shifts and widths of kaonic atoms over the periodic table. We also investigate the region of deeply bound kaonic nuclear states which appear with very large widths in medium and heavy nuclei. Some of the deep atomic states, still unobserved, appear with narrower widths than the separation between levels, which makes them eligible for experimental observation. To this end, we make some estimates of the rates of formation in the ( K − , γ ) reaction.