The extreme rarity of asexual vertebrates in nature is generally explained by genomic decay due to absence of meiotic recombination, thus leading to extinction of such lineages. We explore features of a vertebrate asexual genome, the Amazon molly, Poecilia formosa, and find few signs of genetic degeneration but unique genetic variability and ongoing evolution. We uncovered a substantial clonal polymorphism and, as a conserved feature from its interspecific hybrid origin, a 10-fold higher heterozygosity than in the sexual parental species. These characteristics seem to be a principal reason for the unpredicted fitness of this asexual vertebrate. Our data suggest that asexual vertebrate lineages are scarce not because they are at a disadvantage, but because the genomic combinations required to bypass meiosis and to make up a functioning hybrid genome are rarely met in nature.