The physics, and a design, of a Large Hadron Electron Collider (LHeC) aresketched. With high luminosity, 1033cm-2s-1,and high energy, s1/2=1.4TeV, such a collider can be builtin which a 70GeV electron (positron) beam in the LHC tunnel is in collision with one of the LHC hadron beams and which operates simultaneously with the LHC. The LHeC makes possibledeep-inelastic lepton-hadron (ep, eD and eA) scattering formomentum transfers Q2beyond 106GeV2 and for Bjorken x down to the 10-6.New sensitivity to the existence of new states of matter, primarily inthe lepton-quark sector and in dense partonic systems,is achieved. The precision possible with an electron-hadron experimentbrings in addition crucial accuracy in the determination of hadron structure,as described in Quantum Chromodynamics,and of parton dynamics at the TeV energy scale. The LHeC thus complements the proton-proton and ion programmes,adds substantial new discovery potential to them, and is importantfor a full understanding of physics in the LHC energy range.