Viruses are abundant in the ocean and a major driving force in plankton ecology and evolution. It has been assumed that most of the viruses in seawater contain DNA and infect bacteria, but RNA-containing viruses in the ocean, which almost exclusively infect eukaryotes, have never been quantified. We compared the total mass of RNA and DNA in the viral fraction harvested from seawater and using data on the mass of nucleic acid per RNA- or DNA-containing virion, estimated the abundances of each. Our data suggest that the abundance of RNA viruses rivaled or exceeded that of DNA viruses in samples of coastal seawater. The dominant RNA viruses in the samples were marine picorna-like viruses, which have small genomes and are at or below the detection limit of common fluorescence-based counting methods. If our results are typical, this means that counts of viruses and the rate measurements that depend on them, such as viral production, are significantly underestimated by current practices. As these RNA viruses infect eukaryotes, our data imply that protists contribute more to marine viral dynamics than one might expect based on their relatively low abundance. This conclusion is a departure from the prevailing view of viruses in the ocean, but is consistent with earlier theoretical predictions.