Arctic sea ice has steadily diminished as atmospheric greenhouse gas concentrations have increased. Using observed data from 1979 to 2019, we estimate a close contemporaneous linear relationship between Arctic sea ice area and cumulative carbon dioxide emissions. For comparison, we provide analogous regression estimates using simulated data from global climate models (drawn from the CMIP5 and CMIP6 model comparison exercises). The carbon sensitivity of Arctic sea ice area is considerably stronger in the observed data than in the climate models. Thus, for a given future emissions path, an ice-free Arctic is likely to occur much earlier than the climate models project. Furthermore, little progress has been made in recent global climate modeling (from CMIP5 to CMIP6) to more accurately match the observed carbon-climate response of Arctic sea ice.