Most estimates of the climatically-important transfer of atmospheric gases into, and out of, the ocean assume that the ocean surface is unbroken by breaking waves. However the trapping of bubbles of atmospheric gases in the ocean by breaking waves introduces an asymmetry in this flux. This asymmetry occurs as a bias towards injecting gas into the ocean where it dissolves, and against the evasion/exsolution of previously-dissolved gas coming out of solution from the oceans and eventually reaching the atmosphere. Here we use at-sea measurements and modelling of the bubble clouds beneath the ocean surface to show that the numbers of large bubbles found metres below the sea surface in high winds are sufficient to drive a large and asymmetric flux of carbon dioxide. Our results imply a much larger asymmetry for carbon dioxide than previously proposed. This asymmetry contradicts an assumption inherent in most existing estimates of ocean-atmosphere gas transfer. The geochemical and climate implications include an enhanced invasion of carbon dioxide into the stormy temperate and polar seas.