Neuronal-class diversification is central during neurogenesis. This requirement is exemplified in the olfactory system, which utilizes a large array of olfactory receptor neuron (ORN) classes. We discovered an epigenetic mechanism in which neuron diversity is maximized via locus-specific chromatin modifications that generate context-dependent responses from a single, generally used intracellular signal. Each ORN in Drosophila acquires one of three basic identities defined by the compound outcome of three iterated Notch signaling events during neurogenesis. Hamlet, the Drosophila Evi1 and Prdm16 proto-oncogene homolog, modifies cellular responses to these iteratively used Notch signals in a context-dependent manner, and controls odorant receptor gene choice and ORN axon targeting specificity. In nascent ORNs, Hamlet erases the Notch state inherited from the parental cell, enabling a modified response in a subsequent round of Notch signaling. Hamlet directs locus-specific modifications of histone methylation and histone density and controls accessibility of the DNA-binding protein Suppressor of Hairless at the Notch target promoter.