We present results from an Eulerian adaptive mesh refinement simulation demonstrating the formation of a primordial star within an HII region produced by an earlier massive star. Despite the higher temperatures of the ionized gas, this second star formed within 23 million years of its neighbor's death. The enhanced electron fraction within the HII region catalyzes rapid molecular hydrogen formation, leading to enhanced cooling in the preprocessed halo. This “second generation” primordial protostar has a much lower accretion rate than its predecessor, due in part to the higher angular momentum of the halo in which it forms. This situation may allow binaries or multiple systems of low-mass stars to form. The result discussed here is described in more detail in O'Shea et al. (2005).