A physically anchored consensus map is foundational to modern genomics research; however, construction of such a map in oat (Avena sativa L., 2n = 6x = 42) has been hindered by the size and complexity of the genome, the scarcity of robust molecular markers, and the lack of aneuploid stocks. Resources developed in this study include a modified SNP discovery method for complex genomes, a diverse set of oat SNP markers, and a novel chromosome-deficient SNP anchoring strategy. These resources were applied to build the first complete, physically-anchored consensus map of hexaploid oat. Approximately 11,000 high-confidence in silico SNPs were discovered based on nine million inter-varietal sequence reads of genomic and cDNA origin. GoldenGate genotyping of 3,072 SNP assays yielded 1,311 robust markers, of which 985 were mapped in 390 recombinant-inbred lines from six bi-parental mapping populations ranging in size from 49 to 97 progeny. The consensus map included 985 SNPs and 68 previously-published markers, resolving 21 linkage groups with a total map distance of 1,838.8 cM. Consensus linkage groups were assigned to 21 chromosomes using SNP deletion analysis of chromosome-deficient monosomic hybrid stocks. Alignments with sequenced genomes of rice and Brachypodium provide evidence for extensive conservation of genomic regions, and renewed encouragement for orthology-based genomic discovery in this important hexaploid species. These results also provide a framework for high-resolution genetic analysis in oat, and a model for marker development and map construction in other species with complex genomes and limited resources.