Conflict over Iran's nuclear program, which involves a US-led policy to impose sanctions on Iran, is perceived by each side as a preeminent challenge to its own national security and global peace. Yet, there is little scientific study or understanding of how material incentives and disincentives, such as economic sanctions, psychologically affect the targeted population and potentially influence behaviour. Here we explore the Iranian nuclear program within a paradigm concerned with sacred values. We integrate experiments within a survey of 1997 Iranians. We find that a relatively small but politically significant portion of the Iranian population believes that acquiring nuclear energy has become a sacred value, in the sense that proposed economic incentives and disincentives result in a ``backfire effect'' in which offers of material rewards or punishment lead to increased anger and greater disapproval. This pattern was specific to nuclear energy and did not hold for acquiring nuclear weapons. The present study is the first demonstration of the backfire effect for material disincentives as well as incentives, and on an issue whose apparent sacred nature is recent rather than longstanding.