Wild emmer (Triticum turgidum ssp. dicoccoides) is a progenitor of all cultivated wheat grown today. It has been hypothesized that emmer was domesticated in the Karaca Dağ region in southeastern Turkey. A total of 445 recombinant inbred lines of T. turgidum ssp. durum cv. ‘Langdon’ x wild emmer accession PI 428082 from this region was developed and genotyped with the Illumina 90K single nucleotide polymorphism Infinium assay. A genetic map comprising 2,650 segregating markers was constructed. The order of the segregating markers and an additional 8,264 co-segregating markers in the Aegilops tauschii reference genome sequence was used to compare synteny of the tetraploid wheat with the Brachypodium distachyon, rice, and sorghum. These comparisons revealed the presence of 15 structural chromosome rearrangements, in addition to the already known 4A-5A-7B rearrangements. The most common type was an intra-chromosomal translocation in which the translocated segment was short and was translocated only a short distance along the chromosome. A large reciprocal translocation, one small non-reciprocal translocation, and three large and one small paracentric inversions were also discovered. The use of inversions for a phylogeny reconstruction in the Triticum–Aegilops alliance was illustrated. The genetic map was inconsistent with the current model of evolution of the rearranged chromosomes 4A-5A-7B. Genetic diversity in the rearranged chromosome 4A showed that the rearrangements might have been contemporary with wild emmer speciation. A selective sweep was found in the centromeric region of chromosome 4A in Karaca Dağ wild emmer but not in 4A of T. aestivum. The absence of diversity from a large portion of chromosome 4A of wild emmer, believed to be ancestral to all domesticated wheat, is puzzling.