We report a high-quality draft of the genome sequence of the grey, short-tailed opossum (Monodelphis domestica). As the first metatherian ('marsupial') species to be sequenced, the opossum provides a unique perspective on the organization and evolution of mammalian genomes. Distinctive features of the opossum chromosomes provide support for recent theories about genome evolution and function, including a strong influence of biased gene conversion on nucleotide sequence composition, and a relationship between chromosomal characteristics and X chromosome inactivation. Comparison of opossum and eutherian genomes also reveals a sharp difference in evolutionary innovation between protein-coding and non-coding functional elements. True innovation in protein-coding genes seems to be relatively rare, with lineage-specific differences being largely due to diversification and rapid turnover in gene families involved in environmental interactions. In contrast, about 20% of eutherian conserved non-coding elements (CNEs) are recent inventions that postdate the divergence of Eutheria and Metatheria. A substantial proportion of these eutherian-specific CNEs arose from sequence inserted by transposable elements, pointing to transposons as a major creative force in the evolution of mammalian gene regulation.