Identifying cancer-relevant mutations in noncoding regions is challenging due to the large numbers of such mutations, their low levels of recurrence, and difficulties in interpreting their functional impact. To uncover genes that are dysregulated due to somatic mutations in cis, we build upon the concept of differential allele-specific expression (ASE) and introduce methods to identify genes within an individual's cancer whose ASE differs from what is found in matched normal tissue. When applied to breast cancer tumor samples, our methods detect the known allele-specific effects of copy number variation and nonsense-mediated decay. Further, genes that are found to recurrently exhibit differential ASE across samples are cancer relevant. Genes with cis mutations are enriched for differential ASE, and we find 147 potentially functional noncoding mutations cis to genes that exhibit significant differential ASE. We conclude that differential ASE is a promising means for discovering gene dysregulation due to cis noncoding mutations.