Recent observations have revealed massive galactic molecular outflows that may have the physical conditions (high gas densities) required to form stars. Indeed, several recent models predict that such massive outflows may ignite star formation within the outflow itself. This star-formation mode, in which stars form with high radial velocities, could contribute to the morphological evolution of galaxies, to the evolution in size and velocity dispersion of the spheroidal component of galaxies, and would contribute to the population of high-velocity stars, which could even escape the galaxy. Such star formation could provide $in\; situ$ chemical enrichment of the circumgalactic and intergalactic medium (through supernova explosions of young stars on large orbits), and some models also predict it to contribute substantially to the star-formation rate observed in distant galaxies. Although there exists observational evidence for star formation triggered by outflows or jets into their host galaxy, as a consequence of gas compression, evidence for star formation occurring within galactic outflows is still missing. Here we report spectroscopic observations that unambiguously reveal star formation occurring in a galactic outflow at a redshift of 0.0448. The inferred star-formation rate in the outflow is larger than 15 solar masses per year. Star formation may also be occurring in other galactic outflows, but may have been missed by previous observations owing to the lack of adequate diagnostics.