We used public data on greenhouse-gas emissions and land use to evaluate the potential impact of eliminating animal agriculture on atmospheric greenhouse gas levels, and global warming potential. We first updated estimates of carbon dioxide, methane, and nitrous oxide emissions from livestock and livestock feed production. We used these data, along with recent estimates of the atmospheric carbon dioxide that could be converted by photosynthesis into perennial biomass on land currently engaged in animal agriculture, to develop models of net anthropogenic emissions under food-system scenarios ranging from business as usual to the complete elimination of animal agriculture. We then used simple simulations to project atmospheric levels of these three gases through the end of the century under each scenario. Using cumulative differences in radiative forcing as a measure of the impact of different diets, we found that a gradual transition over the next 15 years to a plant-only diet would have the same effect through the rest of the century as an annual reduction of 28 Gt of CO2 emissions. This would effectively negate 56 percent of global emissions at the current rate of 50 Gt CO2eq per year, with a net negation of 2,200 gigatonnes of CO2 emissions by the year 2100. The climate benefits would accrue rapidly - most in the first few decades, effectively pausing greenhouse-gas accumulation for 30 years. These results establish the replacement of animal agriculture as by far the most powerful option in our arsenal of climate-defense strategies, especially given the urgency of the climate threat. How to orchestrate such a shift to maximize its beneficial environmental, public health, food security, economic and social consequences and minimize potential harms should therefore be at the center of climate policy discussions.