The monogenic and monoallelic expression of only one out of >1000 mouse olfactory receptor (ORs) genes requires the formation of large heterochromatic chromatin domains that sequester the OR gene clusters. Within these domains, intergenic transcriptional enhancers evade heterochromatic silencing and converge into interchromosomal hubs that assemble over the transcriptionally active OR. The significance of this nuclear organization in OR choice remains elusive. Here, we show that transcription factors Lhx2 and Ebf specify OR enhancers by binding in a functionally cooperative fashion to stereotypically spaced motifs that defy heterochromatin. Specific displacement of Lhx2 and Ebf from OR enhancers resulted in pervasive, long-range, and trans downregulation of OR transcription, whereas pre-assembly of a multi-enhancer hub increased the frequency of OR choice in cis. Our data provide genetic support for the requirement and sufficiency of interchromosomal interactions in singular OR choice and generate general regulatory principles for stochastic, mutually exclusive gene expression programs.