Cosmological simulations of Population III star formation suggest an initial mass function (IMF) biased toward very massive stars (M>100Msun) formed in minihalos at redshift z>20, when the cooling is driven by molecular hydrogen. However, this result conflicts with observations of extremely-metal poor (EMP) stars in the Milky Way halo, whose r-process elemental abundances appear to be incompatible with those expected from very massive Population III progenitors. We propose a new solution to the problem in which the IMF of second-generation stars formed at z>10, before reionization, is deficient in sub-solar mass stars, owing to the high cosmic microwave background temperature floor. The observed EMP stars are formed preferentially at z10^{-3.5} Zsun by winds from Population II stars. Our cosmological simulations of dark matter halos like the Milky Way show that current samples of EMP stars can only constrain the IMF of late-time Population III stars, formed at z