This paper shows how uncertainty about liquidity demand can lead to a high degree of dollarization in the banking system. I study a model where the demand for currency in each period is random, and where it is easier for banks to borrow in local currency in times of crisis than in dollars. Banks choose a portfolio composed of local currency, dollars, and real loans. Compared to the anticipated transactions demand for each currency, I show that the bank will hold a relatively large amount of dollars and a relatively small amount of local currency. I also show the existence of a dollarization multiplier : as the anticipated transactions demand for dollars increases, the dollarization of the banking sector increases more than proportionately.