Cooling intense high-energy hadron beams poses a major challenge for modern accelerator physics. The synchrotron radiation emitted from such beams is feeble; even in the Large Hadron Collider (LHC) operating with 7 TeV protons, the longitudinal damping time is about 13 hours. None of the traditional cooling methods seem able to cool LHC-class protons beams. In this Letter, we present a novel method of coherent electron cooling based on a high-gain free-electron laser (FEL). This technique could be critical for reaching high luminosities in hadron and electron-hadron colliders.