Hexaploid oat (Avena sativa L., 2n = 6x = 42) is a member of the Poaceae family and has a large genome (~12.5 Gb) containing 21 chromosome pairs from three ancestral genomes. Physical rearrangements among parental genomes have hindered the development of linkage maps in this species. The objective of this work was to develop a single high-density consensus linkage map that is representative of the majority of commonly grown oat varieties. Data from a cDNA-derived single-nucleotide polymorphism (SNP) array and genotyping-by-sequencing (GBS) were collected from the progeny of 12 biparental recombinant inbred line populations derived from 19 parents representing oat germplasm cultivated primarily in North America. Linkage groups from all mapping populations were compared to identify 21 clusters of conserved collinearity. Linkage groups within each cluster were then merged into 21 consensus chromosomes, generating a framework consensus map of 7202 markers spanning 2843 cM. An additional 9678 markers were placed on this map with a lower degree of certainty. Assignment to physical chromosomes with high confidence was made for nine chromosomes. Comparison of homeologous regions among oat chromosomes and matches to orthologous regions of rice (Oryza sativa L.) reveal that the hexaploid oat genome has been highly rearranged relative to its ancestral diploid genomes as a result of frequent translocations among chromosomes. Heterogeneous chromosome rearrangements among populations were also evident, probably accounting for the failure of some linkage groups to match the consensus. This work contributes to a further understanding of the organization and evolution of hexaploid grass genomes.