Since the 1970s, a number of high-inflation Latin American countries have experienced a persistent process of "dollarization". To interpret some of the stylized facts, this paper presents a simple model in which dollarization reflects the fact that there are costs involved in switching the currency denomination of transactions. The transaction costs of dollarization define a band for the inflation differential within which there will be no incentive to switch between currencies. Above the upper value of the band, the local currency gradually disappears as the economy becomes fully dollarized; below the lower value, de-dollarization occurs.