The evolution of the Earth's climate over the twenty-first century depends on the rate at which anthropogenic carbon dioxide emissions are removed from the atmosphere by the ocean and land carbon cycles. Coupled climate-carbon cycle models suggest that global warming will act to limit the land-carbon sink, but these first generation models neglected the impacts of changing atmospheric chemistry. Emissions associated with fossil fuel and biomass burning have acted to approximately double the global mean tropospheric ozone concentration, and further increases are expected over the twenty-first century. Tropospheric ozone is known to damage plants, reducing plant primary productivity and crop yields, yet increasing atmospheric carbon dioxide concentrations are thought to stimulate plant primary productivity. Increased carbon dioxide and ozone levels can both lead to stomatal closure, which reduces the uptake of either gas, and in turn limits the damaging effect of ozone and the carbon dioxide fertilization of photosynthesis. Here we estimate the impact of projected changes in ozone levels on the land-carbon sink, using a global land carbon cycle model modified to include the effect of ozone deposition on photosynthesis and to account for interactions between ozone and carbon dioxide through stomatal closure. For a range of sensitivity parameters based on manipulative field experiments, we find a significant suppression of the global land-carbon sink as increases in ozone concentrations affect plant productivity. In consequence, more carbon dioxide accumulates in the atmosphere. We suggest that the resulting indirect radiative forcing by ozone effects on plants could contribute more to global warming than the direct radiative forcing due to tropospheric ozone increases.