We report measurements of acoustic phonon emission from a weakly coupled AlAs/GaAs superlattice (SL) under vertical electron transport. The phonons were detected using superconducting bolometers. A peak (resonance) was observed in emission parallel to the SL growth axis when the electrical energy drop per SL period matched the energy of the first SL mini-Brillouin zone-center phonon mode. This peak was mirrored by an increase of the differential conductance of the SL. These results are evidence for stimulated emission of terahertz phonons as previously predicted theoretically and suggest that such a SL may form the basis of a SASER (sound amplification by stimulated emission of radiation) device.