Spatial and temporal cues are required to specify neuronal diversity, but how these cues are integrated in neural progenitors remains unknown. Drosophila progenitors (neuroblasts) are a good model: they are individually identifiable with relevant spatial and temporal transcription factors known. Here we test whether spatial/temporal factors act independently or sequentially in neuroblasts. We used Targeted DamID to identify genomic binding sites of the Hunchback temporal factor in two neuroblasts (NB5-6 and NB7-4) that make different progeny. Hunchback targets were different in each neuroblast, ruling out the independent specification model. Moreover, each neuroblast had distinct open chromatin domains, which correlated with differential Hb-bound loci in each neuroblast. Importantly, the Gsb/Pax3 spatial factor, expressed in NB5-6 but not NB7-4, had genomic binding sites correlated with open chromatin in NB5-6, but not NB7-4. Our data support a model in which early-acting spatial factors like Gsb establish neuroblast-specific open chromatin domains, leading to neuroblast-specific temporal factor binding and the production of different neurons in each neuroblast lineage.