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Climate change and economic inequality are inextricably linked. Despite widespread agreement among researchers and policymakers that a carbon tax is the most efficient mechanism to curb greenhouse gas emissions, such a tax exacerbates inequality since low-income households spend a greater share of their income on carbon-intensive goods. Using Input-Output tables and detailed expenditure data for the United States, we estimate households' carbon footprints and examine the impact of a revenue-neutral tax of $50 per ton of CO2 on multiple forms of inequality. Devoting carbon tax revenue to fund a carbon dividend makes the policy progressive, minimizes redistribution among households of similar means, mitigates group-based inequalities, and benefits 56% of people, including 84% in the bottom half of the distribution. While some researchers have dismissed dividends on efficiency grounds, we show that the double dividend typically associated with labor tax cuts is insufficient to protect the purchasing power of a majority of Americans.