Opioid dependence is a highly heterogeneous disease driven by a variety of genetic and environmental risk factors which have yet to be fully elucidated. We interrogated the effects of opioid dependence on the brain using ChIP-seq to quantify patterns of H3K27 acetylation in dorsolateral prefrontal cortical neurons isolated from 51 opioid-overdose cases and 51 accidental death controls. Among opioid cases, we observed global hypoacetylation and identified 388 putative enhancers consistently depleted for H3K27ac. Machine learning on H3K27ac patterns predicts case-control status with high accuracy. We focus on case-specific regulatory alterations, revealing 81,399 hypoacetylation events, uncovering vast inter-patient heterogeneity. We developed a strategy to decode this heterogeneity based on convergence analysis, which leveraged promoter-capture Hi-C to identify five genes over-burdened by alterations in their regulatory network or "plexus": ASTN2, KCNMA1, DUSP4, GABBR2, ENOX1. These convergent loci are enriched for opioid use disorder risk genes and heritability for generalized anxiety, number of sexual partners, and years of education. Overall, our multi-pronged approach uncovers neurobiological aspects of opioid dependence and captures genetic and environmental factors perpetuating the opioid epidemic.