  The physics, and a design, of a Large Hadron Electron Collider (LHeC) are
sketched. With high luminosity, 10^{33}cm^{-2}s^{-1}, and high energy,
\sqrt{s}=1.4 TeV, such a collider can be built in which a 70 GeV 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 possible
deep-inelastic lepton-hadron (ep, eD and eA) scattering for momentum transfers
Q^2 beyond 10^6 GeV^2 and for Bjorken x down to the 10^{-6}. New sensitivity to
the existence of new states of matter, primarily in the lepton-quark sector and
in dense partonic systems, is achieved. The precision possible with an
electron-hadron experiment brings 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 important for a full understanding of physics in the LHC energy
range.
