This paper explores a rational economic explanation for the much discussed credit card debt puzzle. We set-up and simulate a generalization of the buffer-stock consumption model with longterm revolving debt contracts. In line with US credit card law, lenders can always deny households access to new debt, but they cannot demand immediate repayment of the outstanding balance. Under this assumption it is indeed optimal for households to simultaneously hold positive gross debt and positive gross assets even when the interest rate on the debt is much higher than the return rate on the assets. When the risk of being excluded from new borrowing is positively correlated with unemployment, we are able to explain a substantial share of the observed borrower-saver group and match a high level of liquid net worth.