This paper defines systemic risk as the conditional probability of failure of a large number of financial institutions, and develops maximum likelihood estimators of the term structure of systemic risk in the U.S. financial sector. The estimators are based on a new dynamic hazard model of failure timing that captures the influence of time-varying macro-economic and sector-specific risk factors on the likelihood of failures, and the impact of spillover effects related to missing/unobserved risk factors or the spread of financial distress in a network of firms. In- and out-of-sample tests demonstrate that the fitted risk measures accurately quantify systemic risk for each of several risk horizons and confidence levels, indicating the usefulness of the risk measure estimates for the macro-prudential regulation of the financial system.