The structure of the Baxter adhesive hard sphere fluid is examined using computer simulation. The radial distribution function (which exhibits unusual discontinuities due to the particle adhesion) and static structure factor are calculated with high accuracy over a range of conditions and compared with the predictions of Percus-Yevick theory. We comment on rigidity in percolating clusters and discuss the role of the model in the context of experiments on colloidal systems with short range attractive forces.