Galactose oxidase is a copper-containing enzyme, which catalyses stereospecific oxidation of primary alcohols. The three-dimensional structure of the enzyme has been determined in this study by X-ray crystallography at high resolution. The molecule is almost entirely composed of beta-structures and consists of three domains. The arrangement of 28 beta-strands in the second domain is of particular interest, having seven four-stranded antiparallel beta-sheets with pseudo-sevenfold symmetry. The copper site has square-pyramidal coordination with two histidines, one tyrosine and one exogenous ligand at the equatorial sites and another tyrosine at the axial site. The most intriguing structural feature is a covalent bond between C epsilon 1 of Tyr-272, which is one of the equatorial ligands, and S gamma of Cys-228. This unexpected thioether bond, and Trp-290 stacked above it, strongly supports the presence of a tyrosine free radical in the enzyme as a 'built-in' secondary cofactor. Calculation of the molecular surface shows a small pocket at the copper site and suggests a substrate-binding model, which can explain the substrate specificity. A model for the catalytic mechanism, involving a tyrosine free radical and basic tryptophan, is also proposed.