One of the many counterintuitive things students in a first course on options learn is that premature exercise of an American call option on a nondividend paying stock is a mistake, and that for a dividend-paying stock, early exercise is never rational except just before the stock goes ex-dividend. Efforts to incorporate counterparty credit risk in the calculation have suggested assuming no change in exercise policy and simply discount the projected future cash flows at a higher risky interest rate. Others have argued that counterparty default should never happen with American options because the holder will exercise just before the counterparty defaults and effectively step in front of the other creditors to be paid in full. Klein and Yang show that these ideas are incorrect. Early exercise gives up the option’s time value, so that even when imminent counterparty default is perfectly predictable, there is still a cost to exercise for credit reasons. Moreover, properly taking counterparty risk into account leads to optimal exercise behavior different from that in the nonvulnerable case, so simply discounting the same cash flows at a different rate undervalues the vulnerable option. The difference is particularly important when counterparty risk is wrong-way risk, such that the counterparty’s credit weakens under the same conditions that the option is in the money.