No one can doubt that the United States is currently the leading power in the world, and few at least in America would dispute that it needs to exercise world leadership in some fashion. The great debate is over what kind of leadership this should be and how it should be exercised. This essay offers only one idea, drawn primarily from the history of international politics: the United States has a choice between two modes of political leadership that, though they resemble each other and are often identified or considered interchangeable, nonetheless fundamentally differ in nature, practice, and effects. These are empire and hegemony. For purposes of world order and peace, the lure of empire, specious and inviting, is a mirage; the path of hegemony is genuinely possible and arguably necessary. The two, moreover, are not readily combined or compatible, but lead in contradictory directions. The current American pursuit of empire is undermining the chances for a useful, benign American hegemony, and if carried much further will end up promoting the very Hobbesian disorder it was supposed to prevent or overcome, one avoidable under a sane American hegemony.