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Gene expression is a noisy process: in constant environment and genotype, cell to cell variability occurs because of randomness of biochemical reactions..., Biochemical reactions within individual cells result from the interactions of molecules, typically in small numbers. Consequently, the inherent stochasticity of binding and diffusion processes generates noise along the cascade that leads to the synthesis of a protein from its encoding gene. As a result, isogenic cell populations display phenotypic variability even in homogeneous environments. The extent and consequences of this stochastic gene expression have only recently been assessed on a genome-wide scale, owing, in particular, to the advent of single-cell transcriptomics. However, the evolutionary forces shaping this stochasticity have yet to be unraveled. Here, we take advantage of two recently published data sets for the single-cell transcriptome of the domestic mouse Mus musculus to characterize the effect of natural selection on gene-specific transcriptional stochasticity. We show that noise levels in the mRNA distributions (also known as transcriptional noise) significantly correlate with three-dimensional nuclear domain organization, evolutionary constraints on the encoded protein, and gene age. However, the position of the encoded protein in a biological pathway is the main factor that explains observed levels of transcriptional noise, in agreement with models of noise propagation within gene networks. Because transcriptional noise is under widespread selection, we argue that it constitutes an important component of the phenotype and that variance of expression is a potential target of adaptation. Stochastic gene expression should therefore be considered together with the mean expression level in functional and evolutionary studies of gene expression.