Candidates in primary elections face a trade-off between ideological proximity to the party's base and the probability of winning the general election. I describe conditions under which an incumbent politician provokes the opposition party into nominating more extreme candidates. By moving away from the center, the incumbent can exploit the divisions in the opposition party and improve her reelection prospects, despite hurting her appeal to the median voter in the general election. I identify primaries as an understudied mechanism that drives political polarization in two-party democracies. Furthermore, the analysis fits the observation that reelection-seeking incumbents sometimes move away from the center towards the end of their first term in office. I show that party gatekeeping drives this behavior: with a richer set of candidates, the effect disappears.