We present a DNA library preparation method that has allowed us to reconstruct a high-coverage (30×) genome sequence of a Denisovan, an extinct relative of Neandertals. The quality of this genome allows a direct estimation of Denisovan heterozygosity indicating that genetic diversity in these archaic hominins was extremely low. It also allows tentative dating of the specimen on the basis of "missing evolution" in its genome, detailed measurements of Denisovan and Neandertal admixture into present-day human populations, and the generation of a near-complete catalog of genetic changes that swept to high frequency in modern humans since their divergence from Denisovans.