Operational risk is currently receiving significant media attention, as financial scandals have appeared regularly and multiple events have exceeded one billion dollars in total impact. Regulators have also been devoting attention to this risk, and are finalizing proposals that would require banks to hold capital for potential operational losses. This paper uses newly available loss data to model operational risk at internationally active banks. Our results suggest that the amount of capital held for operational risk will often exceed capital held for market risk, and that the largest banks could choose to allocate several billion dollars in capital to operational risk. In addition to capital allocation decisions, our findings should have a direct impact on the compensation and investment models used by large firms, as well as on the optimal allocation of risk management resources.