Stimulated emission of radiation has not been directly observed in astrophysical situations up to this time. Here we demonstrate that photons from pulsar B1641-45 stimulate pulses of excess 1720-megahertz line emission in an interstellar hydroxyl (OH) cloud. As this stimulated emission is driven by the pulsar, it varies on a few-millisecond time scale, which is orders of magnitude shorter than the quickest OH maser variations previously detected. Our 1612-megahertz spectra are inverted copies of the 1720-megahertz spectra. This "conjugate line" phenomenon enables us to constrain the properties of the interstellar OH line-producing gas. We also show that pulsar signals undergo significantly deeper OH absorption than do other background sources, which confirms earlier tentative findings that OH clouds are clumpier on small scales than are neutral hydrogen clouds.