Although spliceosomal introns are present in all characterized eukaryotes, intron numbers vary dramatically, from only a handful in the entire genomes of some species to nearly 10 introns per gene on average in vertebrates. For all previously studied intron-rich species, significant fractions of intron positions are shared with other widely diverged eukaryotes, indicating that 1) large numbers of the introns date to much earlier stages of eukaryotic evolution and 2) these lineages have not passed through a very intron-poor stage since early eukaryotic evolution. By the same token, among species that have lost nearly all of their ancestral introns, no species is known to harbor large numbers of more recently gained introns. These observations are consistent with the notion that intron-dense genomes have arisen only once over the course of eukaryotic evolution. Here, we report an exception to this pattern, in the intron-rich diatom Thalassiosira pseudonana. Only 8.1% of studied T. pseudonana intron positions are conserved with any of a variety of divergent eukaryotic species. This implies that T. pseudonana has both 1) lost nearly all of the numerous introns present in the diatom-apicomplexan ancestor and 2) gained a large number of new introns since that time. In addition, that so few apparently inserted T. pseudonana introns match the positions of introns in other species implies that insertion of multiple introns into homologous genic sites in eukaryotic evolution is less common than previously estimated. These results suggest the possibility that intron-rich genomes may have arisen multiple times in evolution. These results also provide evidence that multiple intron insertion into the same site is rare, further supporting the notion that early eukaryotic ancestors were very intron rich.