Aegilops tauschii is the diploid progenitor of the D genome of hexaploid wheat1 (Triticum aestivum, genomes AABBDD) and an important genetic resource for wheat2,3,4. The large size and highly repetitive nature of the Ae. tauschii genome has until now precluded the development of a reference-quality genome sequence5. Here we use an array of advanced technologies, including ordered-clone genome sequencing, whole-genome shotgun sequencing, and BioNano optical genome mapping, to generate a reference-quality genome sequence for Ae. tauschii ssp. strangulata accession AL8/78, which is closely related to the wheat D genome. We show that compared to other sequenced plant genomes, including a much larger conifer genome, the Ae. tauschii genome contains unprecedented amounts of very similar repeated sequences. Our genome comparisons reveal that the Ae. tauschii genome has a greater number of dispersed duplicated genes than other sequenced genomes and its chromosomes have been structurally evolving an order of magnitude faster than those of other grass genomes. The decay of colinearity with other grass genomes correlates with recombination rates along chromosomes. We propose that the vast amounts of very similar repeated sequences cause frequent errors in recombination and lead to gene duplications and structural chromosome changes that drive fast genome evolution.