Proton-driven plasma wakefield acceleration is proposed for acceleration of electrons to the TeV frontier in one pass. A new experiment AWAKE will test the idea using the CERN SPS beam injected through 5-10m of plasma. An accompanying external electron pulse will be accelerated from 10MeV with an expected gain of 1GeV. If successful future experiments are envisaged to show 100GeV gain in 100m. This would lead to e+e- and LHeC designs at CERN.