Stem cell asymmetric division requires tight control of spindle orientation. To study this key process, we have recorded Drosophila larval neural stem cells (NBs) engineered to express fluorescent reporters for microtubules, pericentriolar material (PCM), and centrioles. We have found that early in the cell cycle, the two centrosomes become unequal: one organizes an aster that stays near the apical cortex for most of the cell cycle, while the other loses PCM and microtubule-organizing activity, and moves extensively throughout the cell until shortly before mitosis when, located near the basal cortex, it recruits PCM and organizes the second mitotic aster. Upon division, the apical centrosome remains in the stem cell, while the other goes into the differentiating daughter. Apical aster maintenance requires the function of Pins. These results reveal that spindle orientation in Drosophila larval NBs is determined very early in the cell cycle, and is mediated by asymmetric centrosome function.