Expression of vast repertoires of antigen receptors by lymphocytes, with each cell expressing a single receptor, requires stochastic activation of individual variable (V) genes for transcription and recombination. How this occurs remains unknown. Using single-cell RNA sequencing (scRNA-seq) and allelic variation, we show that individual pre-B cells monoallelically transcribe divergent arrays of Vκ genes, thereby opening stochastic repertoires for subsequent Vκ-Jκ recombination. Transcription occurs upon translocation of Vκ genes to RNA polymerase II arrayed on the nuclear matrix in transcription factories. Transcription is anchored by CTCF-bound sites or E2A-loaded Vκ promotors and continues over large genomic distances delimited only by topological associating domains (TADs). Prior to their monoallelic activation, Vκ loci are transcriptionally repressed by cyclin D3, which prevents capture of Vκ gene containing TADs by transcription factories. Cyclin D3 also represses protocadherin, olfactory, and other monoallelically expressed genes, suggesting a widely deployed mechanism for coupling monoallelic gene activation with cell cycle exit.