Olfactory receptor (OR) choice represents an example of genetically hardwired stochasticity, where every olfactory neuron expresses one out of ~2000 OR alleles in a probabilistic, yet stereotypic fashion. Here, we show that topographic restrictions in OR expression are established in neuronal progenitors by two opposing forces: polygenic transcription and genomic silencing, both of which are influenced by dorsoventral gradients of transcription factors NFIA, B, and X. Polygenic transcription defines spatially constrained OR repertoires, among which one OR allele may be selected for singular expression later in development. Heterochromatin assembly and genomic compartmentalization preferentially eliminate from this “privileged” repertoire ORs with more dorsal expression destinations, which are ectopically transcribed in neuronal progenitors throughout the olfactory epithelium. Our experiments identify early transcription as an “epigenetic” contributor to future developmental patterning and reveal how two spatially responsive probabilistic processes act in concert to establish deterministic, precise, and reproducible territories of stochastic gene expression.