Based on current CERN infrastructure, an electron--proton collider is proposed at a center-of-mass energy of about 9 TeV. A 7 TeV LHC bunch is used as the proton driver to create a plasma wakefield which then accelerates electrons to 3 TeV, these then colliding with the other 7 TeV LHC proton beam. Although of very high energy, the collider has a modest projected integrated luminosity of 10-100 inverse pb. For such a collider, with a center-of-mass energy 30 times greater than HERA, parton momentum fractions, x, down to about 10^-8 are accessible for photon virtualities, Q^2, of 1 GeV^2. The energy dependence of hadronic cross sections at high energies, such as the the total photon-proton cross section, which has synergy with cosmic-ray physics, can be measured and QCD and the structure of matter better understood in a region where the effects are completely unknown. Searches at high Q^2 for physics beyond the Standard Model will be possible, in particular the significantly increased sensitivity to the production of leptoquarks.