Surface plasmons (SPs) are surface-bound electromagnetic waves supported by metals, offering the possibility of strong spatial confinement of electromagnetic fields on the micro- and nanoscales. They suffer, however, from strong damping caused by internal absorption and radiation losses. Here we demonstrate amplification of SPs by stimulated emission, which marks a possible solution to this problem. We use an attenuated-total-reflection setup to detect stimulated emission of SPs at the interface between a silver film and an optically pumped dye solution acting as the amplifying medium. Clear evidence of stimulated emission is provided by an excellent agreement of the experimental observations with a theoretical analysis. Amplification of SPs can be considered analogous to photon amplification in a laser, thereby suggesting novel approaches in the field of nano-optics.