Whole-genome sequence data from samples of natural populations provide fertile grounds for analyses of intraspecific variation and tests of population genetic theory. We show that the urochordate Ciona savignyi, one of the species of ocean-dwelling broadcast spawners commonly known as sea squirts, exhibits the highest rates of single-nucleotide and structural polymorphism ever comprehensively quantified in a multicellular organism. We demonstrate that the cause for the extreme heterozygosity is a large effective population size, and, consistent with prediction by the neutral theory, we find evidence of strong purifying selection. These results constitute in-depth insight into the dynamics of highly polymorphic genomes and provide important empirical support of population genetic theory as it pertains to population size, heterozygosity, and natural selection.