Structured diffuse scattering has been observed in selected area electron diffraction patterns of PbZr1-xTixO3 (PZT). This scattering is most evident in the rhombohedral (Zr-rich) phase but has also been observed for a range of compositions including in the important morphotropic phase boundary (MPB) region as well as in the tetragonal (Ti-rich) phase. Monte Carlo computer simulation has been used to show that the scattering originates from the correlation between the displacements of cations in chains running along all four of the cubic <111>c directions. The transverse polarised nature of the scattering means that the ionic shifts are also directed along <111>c. The results are difficult to reconcile with current structural models for the low temperature phases of PZT. It is conjectured that these phases must still contain significant remnants of the disorder present in the high-temperature paraelectric cubic phase.