The generation of cellular diversity is essential in embryogenesis, especially in the central nervous system. During neurogenesis, cell interactions or asymmetric protein localization during mitosis can generate daughter cells with different fates. Here we describe the asymmetric localization of a messenger RNA and an RNA-binding protein that creates molecular and developmental differences between Drosophila neural precursors (neuroblasts) and their daughter cells, ganglion mother cells (GMCs). The prospero (pros) mRNA and the RNA-binding protein Staufen (Stau) are asymmetrically localized in mitotic neuroblasts and are specifically partitioned into the GMC, as is Pros protein. Stau is required for localization of pros RNA but not of Pros protein. Loss of localization of Stau or of pros RNA alters GMC development, but only in embryos with reduced levels of Pros protein, suggesting that pros RNA and Pros protein act redundantly to specify GMC fate. We also find that GMCs do not transcribe the pros gene, showing that inheritance of pros RNA and/or Pros protein from the neuroblast is essential for GMC specification.