Many terrorist factions care about the level of popular support they enjoy within a population they claim to represent. Empirically, this level of support can either rise or fall in the aftermath of a campaign of terrorist violence. Under what circumstances is the use of terror an effective tactic for mobilizing political support for an extremist group? This article models a scenario in which an extremist faction considers attacking a government in the hopes of provoking a counterterror response that will radicalize the population, increasing the extremists' support at the expense of a more moderate faction. In our scenario, such radicalization can result either from the economic damage caused by counterterror operations or by the way in which such operations change the population's assessment of the government's motivations. We demonstrate that such attempts at mobilizing public support can be, but need not be, successful, discuss factors that make both the initiation of a terror campaign and successful mobilization more or less likely, and relate our results to several empirical cases.