Donkeys and horses share a common ancestor dating back to about 4 million years ago. Although a high-quality genome assembly at the chromosomal level is available for the horse, current assemblies available for the donkey are limited to moderately sized scaffolds. The absence of a better-quality assembly for the donkey has hampered studies involving the characterization of patterns of genetic variation at the genome-wide scale. These range from the application of genomic tools to selective breeding and conservation to the more fundamental characterization of the genomic loci underlying speciation and domestication. We present a new high-quality donkey genome assembly obtained using the Chicago HiRise assembly technology, providing scaffolds of subchromosomal size. We make use of this new assembly to obtain more accurate measures of heterozygosity for equine species other than the horse, both genome-wide and locally, and to detect runs of homozygosity potentially pertaining to positive selection in domestic donkeys. Finally, this new assembly allowed us to identify fine-scale chromosomal rearrangements between the horse and the donkey that likely played an active role in their divergence and, ultimately, speciation.