The geometric structure of O/Fe(001)-p(1x1) is studied by surface X-ray diffraction (SXRD). After dosing of about 4 L (1 L=10⁻⁶ Torr s) of oxygen at room temperature we find approximately one monolayer (ML) of oxygen in an FeO-like structure forming two layer thick islands covering about 40% of a roughened Fe(001) surface. Subsequent annealing up to 500 ^°C results in surface flattening leading to a highly ordered structure. Very precise SXRD data reveal the presence of 1 ML of oxygen atoms located in fourfold hollow sites at d(O-Fe)=0.48±0.08 Å above the first Fe layer. The first Fe-Fe-interlayer spacing is expanded to d12=1.66±0.02 Å corresponding to an increase of 16% relative to the bulk spacing (1.43 Å). Density-functional calculations confirm our findings and indicate a strong dependence of the (local) layer expansion on the oxygen coverage. Our results are important for understanding the surface magnetic properties of the O/Fe(001)-p(1x1) surface in general.