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Adsorption of 0.25 ML oxygen on the Cu{100}-c(2x2)-Pt surface alloy followed by a brief thermal activation to 500 K and recooling to room temperature leads to the formation of a surface structure with a p(2x2) periodicity. The structure of this Pt/Cu{100}-(2x2)-O has been determined by quantitative low energy electron diffraction (LEED) calculations using the symmetrised automated tensor LEED (SATLEED) program. The results of the calculations suggest that simple p(2x2) overlayers can be ruled out in favour of an oxygen-induced surface reconstruction. The favoured model (Pendry R-factor=0.23) consists of a mixed c(2x2) CuPt underlayer below a reconstructed Cu{100} outermost layer with oxygen atoms occupying a slightly displaced fourfold hollow sites above second layer Pt atoms relative to the original unreconstructed surface.