Extensive cell-to-cell variation exists even among putatively identical cells, and there is great interest in understanding how the properties of transcription relate to this heterogeneity. Differential expression from the two gene copies in diploid cells could potentially contribute, yet our ability to measure from which gene copy individual RNAs originated remains limited, particularly in the context of tissues. Here, we demonstrate quantitative, single molecule allele-specific RNA FISH adapted for use on tissue sections, allowing us to determine the chromosome of origin of individual RNA molecules in formaldehyde-fixed tissues. We used this method to visualize the allele-specific expression of Xist and multiple autosomal genes in mouse kidney. By combining these data with mathematical modeling, we evaluated models for allele-specific heterogeneity, in particular demonstrating that apparent expression from only one of the alleles in single cells can arise as a consequence of low-level mRNA abundance and transcriptional bursting.