Measurement of high-Q2 neutral current deep inelastic scattering e+p cross sections with longitudinally polarised positrons with ZEUS at HERA The cross sections for neutral current deep inelastic scattering in e+p collisions with a longitudinally polarised positron beam were measured using the ZEUS detector at HERA. The results, based on data corresponding to an integrated luminosity of 140 pb-1 at sqrt{s}=318 GeV, are given for both positive and negative values of the longitudinal polarisation of the positron beam. Single differential cross sections in Q2, x and y and double differential cross sections in Q2 and x are shown in the kinematic the kinematic region Q2>185 GeV2. The measured cross sections are compared to the predictions of the Standard Model.