  We study star formation within outflows driven by active galactic nuclei
(AGN) as a new source of hypervelocity stars (HVSs). Recent observations
revealed active star formation inside a galactic outflow at a rate of $\sim
15\,M_{\odot}\,\rm yr^{-1}$. We verify that the shells swept up by an AGN
outflow are capable of cooling and fragmentation into cold clumps embedded in a
hot tenuous gas via thermal instabilities. We show that cold clumps of $\sim
10^3\,M_{\odot}$ are formed within $\sim 10^5$ yrs. As a result, stars are
produced along outflow's path, endowed with the outflow speed at their
formation site. These HVSs travel through the galactic halo and eventually
escape into the intergalactic medium. The expected instantaneous rate of star
formation inside the outflow is $\sim 4-5$ orders of magnitude greater than the
average rate associated with previously proposed mechanisms for producing HVSs,
such as the Hills mechanism and three-body interaction between a star and a
black hole binary. We predict the spatial distribution of HVSs formed in AGN
outflows for future observational probe.
