Graded Hedgehog (Hh) signaling patterns the spinal cord dorsoventral axis by inducing and positioning distinct precursor domains, each of which gives rise to a different type of neuron. These domains also generate glial cells, but the full range of cell types that any one precursor population produces and the mechanisms that diversify cell fate are unknown. By fate mapping and clonal analysis in zebrafish, we show that individual ventral precursor cells that express olig2 can form motoneurons, interneurons and oligodendrocytes. However, olig2+ precursors are not developmentally equivalent, but instead produce subsets of progeny cells in a spatially and temporally biased manner. Using genetic and pharmacological manipulations, we provide evidence that these biases emerge from Hh acting over time to set, maintain, subdivide and enlarge the olig2+ precursor domain and subsequently specify oligodendrocyte development. Our studies show that spatial and temporal differences in Hh signaling within a common population of neural precursors can contribute to cell fate diversification.