The p(1 x 1) adsorption of atomic oxygen on the fee and hcp three-fold hollow site of a Pt(lll) surface has been investigated by a periodic slab model, varying the number of layers from two to four. The density functional method with local spin density approximation and with generalized gradient exchange-correlation functionals was employed using the CRYSTAL95 ab initio program. It was found that the three-layer slab model was a good compromise between accuracy and the computational time. The LDA/VWN calculations predict that the fee-hollow site is energetically preferable by 0.29 eV compared to the hcp-hollow site. This preference is also supported by experimental data. Oxygen p(1 x 1) heat of adsorption of 0.61 eV calculated with the BPW91 method is in reasonable agreement with the experimentally estimated one. The corresponding equilibrium adsorbate-surface distance is 1.25 Angstrom. Density-of-states analysis demonstrates that the formation of the Pt-O bond is mainly due to the interaction of Pt 5d(xz) and 5d(yx) orbitals of the surface platinum atom and 2p(x) and 2p(y) orbitals of the oxygen adatom. Three-dimensional difference electron density plots indicate a delocalized interaction of the oxygen adatoms to the surface.