Single molecule RNA FISH techniques have enabled the quantification of gene expression at the single cell level, revealing significant variability that has been previously obscured by techniques measuring population averages. These techniques, however, have been limited in that they cannot classify transcripts according to their allele of origin. In this thesis, we expand single molecule RNA FISH so that it can discriminate between single nucleotide differences on individual transcripts, enabling single cell allele specific expression. We derive an extensive statistical framework for the analysis of our technique, designated SNP-FISH, and explore the effect of varying many of its experimental parameters. We show how SNP-FISH can inform biological regulation by directly distinguishing cis and trans variability and can be applied to a wide range of biological questions. We then leverage SNP-FISH in the study of imprinting dysregulation. Humans with imprinting disorders have been known to present with highly variable phenotypic severity, and it was thought that these diferences might arise at the single-cell level. By applying SNP-FISH in an imprinting mouse mutant, we show that a partial deletion of methylation sites in the imprinting control region leads to epigenetic mosaicism, with some cells remaining effectively wild type with retained methylation while others are fully mutant with total loss of methylation. In showing this, we expanded SNP-FISH to work in tissues and developed a protocol for clonal bisulfite analysis of primary cells. Ultimately, our work shows how stochastic decisions by single cells can underlie disease severity.