The recent proliferation of bitcoin has been a boon for users but might pose problems for governments. Indeed, some governments have already taken steps to ban or discourage the use of bitcoin. In a model with endogenous matching and random consumption preferences, we find multiple monetary equilibria including one in which bitcoin coexists with official currency. We then identify the conditions under which government transactions policy might deter the use of bitcoin. We show that such a policy becomes more difficult if some users strictly prefer bitcoin because they can avoid other users holding the official currency in the matching process. (JEL C78, E41, E42, E50)