Measurement of Charged Current Deep Inelastic Scattering Cross Sections with a Longitudinally Polarised Electron Beam at HERA ZEUS Collaboration Measurements of the cross sections for charged current deep inelastic scattering in e-p collisions with longitudinally polarised electron beams are presented. The measurements are based on a data sample with an integrated luminosity of 175pb^-1 collected with the ZEUS detector at HERA at a centre-of-mass energy of 318 GeV. The total cross section is given for positively and negatively polarised electron beams. The differential cross-sections dsigma/dQ2, dsigma/dx and dsigma/dy are presented for Q2>200 GeV2. The double-differential cross-section d^2sigma/dxdQ2 is presented in the kinematic range 280