This paper analyzes the contagion channels through which a Greek credit event would spread to the rest of the European Union and then to the United States. A credit crisis would be manifested as a shortage of liquidity, but the real cause would be bank credit risk, which would infect simultaneously the interbank, repo, and certificates of deposits markets. It would then infect the credit default swaps market and money market funds markets. In the past, the risk of a run on the banks was triggered by a purely random event, but nowadays the risk of a run on the entire financial system (whether traditional or shadow) has become systemic. This change in the nature of the risk is due to the excess liquidity in the world financial system. The more excessive the liquidity is, the higher the is probability that the risk will turn out to be systemic. The possibility that a Greek credit event can trigger a Lehman Brothers type of incident in the world financial system is high because the euro zone is not an optimum currency area and because EU policymakers treat it as an illiquidity rather than insolvency problem, which requires capital transfers. Despite this predicament, the losses of financial institutions are likely to be smaller than those triggered by Lehman Brothers because the risk appetite for risky assets is small and the degree of asset leverage is low, around 20 times equity capital, compared with 55 at the time of the Lehman Brothers collapse.