Many have observed that political candidates running for election are often purposefully expressing themselves in vague and ambiguous terms. Moreover, the candidates' ambiguity typically involves precisely those issues which stand in the center of public debate. In this paper, we provide a simple formal model of this phenomenon. We assume that candidates prefer to be ambiguous, at least as long as it does not impair their chances to be elected. One reason for their preference for ambiguity is that the more ambiguous a candidate is, the less he is committed to specific policies when in office, and the more freedom he has when confroting unforeseen contingencies. We model the electoral competition between two candidates as a two-stage game. In the first stage of the game, the candidates simultaneously choose their ideologies, and in the second stage of the game, they simulataneously choose their level of ambiguity. Our results show that an equilibrium always exists, and the two candidates always choose the same level of strategic ambiguity. We find that for certain ranges of parameter values, both candidates will express themselves in ambiguous terms. More interestingly, the candidates may find it advantageous to differentiate themselves ideologically. Thus, we show the existence of an equilibrium where one candidate chooses, say, a "leftist" ideology, the other candidate chooses a "centrist" ideology and both candidates remain vague regarding their future policies in case they win the election.