It was first suggested by Gold in 1948  that the exquisite sensitivity and frequency selectivity of the mammalian cochlea is due to an active process referred to as the cochlear amplifier. It is thought that this process works by pumping energy to augment the otherwise damped sound-induced vibrations of the basilar membrane [2-4], a mechanism known as negative damping. The existence of the cochlear amplifier has been inferred from comparing responses of sensitive and compromised cochleae  and observations of acoustic emissions [6, 7] and through mathematical modeling [8, 9]. However, power amplification has yet to be demonstrated directly. Here, we prove that energy is indeed produced in the cochlea on a cycle-by-cycle basis. By using laser interferometry , we show that the nonlinear component of basilar-membrane responses to sound stimulation leads the forces acting on the membrane. This is possible only in active systems with negative damping . Our finding provides the first direct evidence for power amplification in the mammalian cochlea. The finding also makes redundant current hypotheses of cochlear frequency sharpening and sensitization that are not based on negative damping.