Chromosome separation and segregation must be executed within a bacterial cell in which the membrane and cytoplasm are highly structured. Here, we develop a strand-specific model based on each of the future daughter chromosomes being associated with a different set of structures or hyperstructures in an asymmetric cell. The essence of the segregation mechanism is that the genes on the same strand in the parental cell that are expressed together in a hyperstructure continue to be expressed together and segregate together in the daughter cell. The model therefore requires an asymmetric distribution of classes of genes and of binding sites and other structures on the strands of the parental chromosome. We show that the model is consistent with the asymmetric distribution of highly expressed genes and of stress response genes in Escherichia coli and Bacillus subtilis. The model offers a framework for interpreting data from genomics.