In this essay I analyze and defend the common sense moral conviction that terrorism, i.e., the use of violence against civilians for political or military purposes, is always morally impermissible. Terrorism violates the fundamental moral prohibition against harming the innocent, even to produce greater overall good. It is therefore just the sort of case that serves as a refutation of consequentialist moral theories. From a deontological perspective, the only remotely plausible forms of justification for a terrorist act would be that it constitutes a form of justifiable punishment of the guilty, or that it is legitimate self-defense against an aggressor. But an examination of the fundamental moral and legal principles of punishment and self-defense demonstrates that neither of these claims can succeed. Since terrorism cannot be justified either as punishment or as self-defense, it cannot be morally justified at all.