WAVE breaking transfers momentum from the atmosphere (winds) to the ocean (currents) 1,2 and entrains air in bubbles which are believed to generate and scatter underwater sound 3-5. Wave breaking and the associated entrainment of air in bubbles are also thought to be important in heat and gas transfer across the air-sea interface 6-8, but the lack of detailed measurements of air entrainment in bubbles has impeded our understanding of the effect of wave breaking on these processes. Here we present measurements of air entrainment by controlled deep-water breaking waves, which show that the bubble plumes generated by breaking waves contain volume fractions of air that are many orders of magnitude greater than expected. Bubble plumes with such large void fractions may be the source of low-frequency sound in the ocean 9. We conclude that the processes of surface-wave evolution and air entrainment are dynamically coupled, and that the contribution of bubbles to air-sea gas transfer and to sound propagation may be seriously underestimated if the existence of these plumes of large bubbles is not taken into account.