Unraveling how regulatory divergence contributes to species differences and adaptation requires identifying functional variants from among millions of genetic differences. Analysis of allelic imbalance (AI) reveals functional genetic differences in cis regulation and has demonstrated differences in cis regulation within and between species. Regulatory mechanisms are often highly conserved, yet differences between species in gene expression are extensive. What evolutionary forces explain widespread divergence in cis regulation? AI was assessed in Drosophila melanogaster-Drosophila simulans hybrid female heads using RNA-seq technology. Mapping bias was virtually eliminated by using genotype-specific references. Allele representation in DNA sequencing was used as a prior in a novel Bayesian model for the estimation of AI in RNA. Cis regulatory divergence was common in the organs and tissues of the head with 41% of genes analyzed showing significant AI. Using existing population genomic data, the relationship between AI and patterns of sequence evolution was examined. Evidence of positive selection was found in 30% of cis regulatory divergent genes. Genes involved in defense, RNAi/RISC complex genes, and those that are sex regulated are enriched among adaptively evolving cis regulatory divergent genes. For genes in these groups, adaptive evolution may play a role in regulatory divergence between species. However, there is no evidence that adaptive evolution drives most of the cis regulatory divergence that is observed. The majority of genes showed patterns consistent with stabilizing selection and neutral evolutionary processes.