Bdelloid rotifers are notorious as a speciose ancient clade comprising only asexual lineages. Thanks to their ability to repair highly fragmented DNA, most bdelloid species also withstand complete desiccation and ionizing radiation. Producing a well-assembled reference genome is a critical step to developing an understanding of the effects of long-term asexuality and DNA breakage on genome evolution. To this end, we present the first high-quality chromosome-level genome assemblies for the bdelloid Adineta vaga, composed of six pairs of homologous (diploid) chromosomes with a footprint of paleotetraploidy. The observed large-scale losses of heterozygosity are signatures of recombination between homologous chromosomes, either during mitotic DNA double-strand break repair or when resolving programmed DNA breaks during a modified meiosis. Dynamic subtelomeric regions harbor more structural diversity (e.g., chromosome rearrangements, transposable elements, and haplotypic divergence). Our results trigger the reappraisal of potential meiotic processes in bdelloid rotifers and help unravel the factors underlying their long-term asexual evolutionary success.