We use data from the Survey of Consumer Finance and Survey of Income Program Participation to show that young households with children are under-insured against the risk that an adult member of the household dies. We develop a tractable macroeconomic model with human capital risk, age-dependent returns to human capital investment, and endogenous borrowing constraints due to the limited pledgeability of human capital (limited contract enforcement). We show analytically that, consistent with the life insurance data, in equilibrium young households are borrowing constrained and under-insured against human capital risk. A calibrated version of the model can quantitatively account for the life-cycle variation of life-insurance holdings, financial wealth, earnings, and consumption inequality observed in the US data. Our analysis implies that a reform that makes consumer bankruptcy more costly, like the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005, leads to a substantial increase in the volume of both credit and insurance.