We provide a novel decomposition of changing gaps in life expectancy between rich and poor into differential changes in age-specific mortality rates and differences in "survivability". Declining age-specific mortality rates increases life expectancy, but the gain is small if the likelihood of living to this age is small (ex ante survivability) or if the expected remaining lifetime is short (ex post survivability). Lower survivability of the poor explains between one-third and one-half of the recent rise in life expectancy inequality in the US and the entire change in Denmark. Our analysis shows that the recent widening of mortality rates between rich and poor due to lifestyle-related diseases does not explain much of the rise in life expectancy inequality. Rather, the dramatic 50% reduction in cardiovascular deaths, which benefited both rich and poor, made initial differences in lifestyle-related mortality more consequential via survivability.