Measurement of high-Q2 charged current deep inelastic scattering e+p cross sections with longitudinally polarised positrons in ZEUS at HERA The cross sections for charged 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. The differential cross sections d#/dQ2, d#/dx and d#/dy for Q2>200 GeV2 are presented. In addition d2#/dxdQ2 was measured in the kinematic range 280 GeV2 < Q2 < 30000 GeV2 and 0.015 < x < 0.65. The measured cross sections are compared to the predictions of the Standard Model.