Famous cultural monuments are often regarded as unique icons, making them an attractive target for terrorists. Despite huge military and police outlays, terrorist attacks on important monuments can hardly be avoided. We argue that an effective strategy to discourage terrorist attacks on iconic monuments is for a government to show a firm commitment to swift reconstruction. Using a simple game‐theoretic model, we demonstrate how a credible claim to rebuild any destroyed cultural monument discourages terrorist attacks by altering the terrorists' expectations and by increasing the government's reputation costs if they fail to rebuild.