Owing to the size mismatch between light and nanoscale objects such as single molecules, it is important to be able to control light-molecule interactions(1-4). Plasmonic nanoantennas create highly enhanced local fields when pumped resonantly, leading to increased Raman scattering(5), but whether fluorescence enhancement occurs depends upon a variety of factors. Although sharp metal tips(6) and colloids(7,8) can enhance fluorescence, the highly enhanced optical fields of lithographically fabricated bowtie nanoantennas(9) provide a structure that is more controllable and amenable to integration. Using gold bowties, we observe enhancements of a single molecule's fluorescence up to a factor of 1,340, ten times higher than reported previously(7,8,10-22). Electromagnetic simulations reveal that this is a result of greatly enhanced absorption and an increased radiative emission rate, leading to enhancement of the intrinsic quantum efficiency by an estimated factor of nine, despite additional non-radiative ohmic effects. Bowtie nanoantennas thus show great potential for high-contrast selection of single nanoemitters.