Neutron diffraction data on the aqueous system dimethyl sulfoxide (DMSO) in water at a concentration of 2 water molecules to 1 DMSO molecule are presented. The hydrogen/deuterium substitution technique is used to extract the HH (water-H to water-H) pair correlation function, g(HH)(r), the MM (methyl-H to methyl-H) correlation function, g(MM)(r), and the MH (methyl-H to water-H) correlation function, g(MH)(r). In addition, three composite pair correlation functions are extracted from the data : XH, which represents the correlation of water hydrogens with nonsubstituted atoms (dominated by the hydrogen bond correlation); XM, which represents the correlation of methyl hydrogens to nonsubstituted atoms (and, therefore, gives information on nonpolar group hydration); and XX, which represents a weighted sum of nonsubstituted atom correlations. The results, together with assumed molecular geometries and expected constraints on atomic overlap, are used to perform a computer simulation of the structure of the solution. This simulated structure is compared, via the site-site pair correlation functions, with the predictions of a recent molecular dynamics simulation of the same system. The results show the pronounced contrast in structure of the water of hydration around DMSO, with the oxygen atom strongly hydrogen-bonded, but the methyl groups surrounded by a loose, hydrogen-bonded cage of water molecules. There is no evidence for the hydrophobic association of DMSO molecules that has been suggested to occur in this system. The data indicate that while the degree of hydrogen bond bending is greater in the solution compared to pure water, the water structure, as measured by the heights of peaks in the pair correlation functions, is more pronounced than in the pure Liquid. This enhanced water structure is associated with the strong hydrogen bonding of water to the DMSO oxygen atom, rather than with the hydrophobic hydration of water molecules with the methyl groups.