High-resolution genetic and physical maps are invaluable tools for building accurate genome assemblies, and interpreting results of genome-wide association studies (GWAS). Previous genetic and physical maps anchored good quality draft assemblies of the domestic cat genome, enabling the discovery of numerous genes underlying hereditary disease and phenotypes of interest to the biomedical science and breeding communities. However, these maps lacked sufficient marker density to order thousands of shorter scaffolds in earlier assemblies, which instead relied heavily on comparative mapping with related species. A high-resolution map would aid in validating and ordering chromosome scaffolds from existing and new genome assemblies. Here, we describe a high-resolution genetic linkage map of the domestic cat genome based on genotyping 453 domestic cats from several multi-generational pedigrees on the Illumina 63K SNP array. The final maps include 58,055 SNP markers placed relative to 6637 markers with unique positions, distributed across all autosomes and the X chromosome. Our final sex-averaged maps span a total autosomal length of 4464 cM, the longest described linkage map for any mammal, confirming length estimates from a previous microsatellite-based map. The linkage map was used to order and orient the scaffolds from a substantially more contiguous domestic cat genome assembly (Felis catus v8.0), which incorporated ~20 × coverage of Illumina fragment reads. The new genome assembly shows substantial improvements in contiguity, with a nearly fourfold increase in N50 scaffold size to 18 Mb. We use this map to report probable structural errors in previous maps and assemblies, and to describe features of the recombination landscape, including a massive (~50 Mb) recombination desert (of virtually zero recombination) on the X chromosome that parallels a similar desert on the porcine X chromosome in both size and physical location.