The zebra mussel, Dreissena polymorpha, continues to spread from its native range in Eurasia to Europe and North America, causing billions of dollars in damage and dramatically altering invaded aquatic ecosystems. Despite these impacts, there are few genomic resources for Dreissena or related bivalves. Although the D. polymorpha genome is highly repetitive, we have used a combination of long-read sequencing and Hi-C-based scaffolding to generate a high-quality chromosome-scale genome assembly. Through comparative analysis and transcriptomics experiments, we have gained insights into processes that likely control the invasive success of zebra mussels, including shell formation, synthesis of byssal threads, and thermal tolerance. We identified multiple intact steamer-like elements, a retrotransposon that has been linked to transmissible cancer in marine clams. We also found that D. polymorpha have an unusual 67 kb mitochondrial genome containing numerous tandem repeats, making it the largest observed in Eumetazoa. Together these findings create a rich resource for invasive species research and control efforts.