The Neotropical brown stink bug, Euschistus heros, is a major pest of soybean in South America. The importance of E. heros as a pest has grown significantly in recent times due to increases in its abundance and range, and the evolution of insecticide resistance. Recent work has begun to examine the genetic diversity, population structure, and genetic mechanisms of insecticide resistance in E. heros. However, to date, investigation of these topics has been hampered by a lack of genomic resources for this species. Here we address this need by assembling a high-quality draft genome for E. heros. We used a combination of short and long read sequencing to assemble an E. heros genome of 1.4 Gb comprising 906 contigs with a contig N50 of 3.5 MB. We leveraged this new genomic resource, in combination with genotyping by sequencing, to explore genetic diversity in populations of this species in Brazil and identify genetic loci in the genome which are under selection. Our genome-wide analyses, confirm that there are two populations of E. heros co-occurring in different geographical regions in Brazil, and that, in certain regions of the country these populations are hybridizing. We identify several regions of the genome as under selection, including markers associated with putative insecticide resistance genes. Taken together, the new genomic resources generated in this study will accelerate research into fundamental aspects of stinkbug biology and applied aspects relating to the sustainable control of a highly damaging crop pest.