Oxygen molecules on Ag(0 0 1), adsorbed at about 60 K, are found to form two-dimensional c(2×4) compact islands. We determine binding site and orientation of the molecules within the superstructure by comparing experimental and calculated scanning tunneling images in combination with molecular dynamics simulations. The molecule adsorbs in the thermodynamically stable fourfold hollow site with its molecular axis in the direction of short periodicity of the superstructure. Rehybridization of 1π and 2π orbitals on adsorption is at the origin of the observed image contrast.