Full three-dimensional diffuse neutron scattering data have been recorded from a single crystal of Pb(Zn1/3Nb2/3) O-3 (PZN) at 300 Kusing the time-of-flight Laue technique on the SXD single-crystal instrument at ISIS. The data show a series of diffuse rods of scattering oriented parallel to each of the six  crystal directions. Monte Carlo simulation has been used to demonstrate that the diffuse rods are caused by planar nanodomains oriented normal to the  directions. Within these domains, there are correlated displacements of the atoms away from their average site positions. In order to explain the systematic absence of some rods of scattering in the ( h k 1) data but the presence of all rods in the ( h k 0) data, it is necessary that the displacement of an O atom is of opposite sign to that of its neighbouring Pb atoms. This is explained in terms of a model based on the fact that Pb2+ possesses a lone pair of electrons, giving the Pb ion directionality.