We propose a model of social norms changing in response to evolving privately held preferences. Our aim is to rationalize the tendency for individuals who hold minority preferences to take actions favored by the majority. We do this using a game involving a tension between a desire to act according to one's underlying preferences and a desire to conform to the majority opinion. We find that even after a majority of the population shares what was previously a minority opinion, members of the new majority are slow to change their behavior. The timing and speed with which behavior transitions to match new, majority-held opinions depends on the size of the reward for conformity. When the rewards for conformity are low, the transition is gradual, with considerable periods of costly public disagreement. When the rewards for conformity are high, transitions are slow to start but conclude rapidly once they begin.