The attacks on September 11th brought terrorism home for the American public and fear over nuclear weapons have been present since the first atomic bombing in August of 1945. These two combined are the explicit fear of a number of national security experts and the international community as a whole. But how warranted are these fears over nuclear terrorism? This paper examines the likelihood of a terrorist organization pursuing and acquiring nuclear weapons and finds it to be very low for a number of reasons. First, the desire of terrorist groups to acquire nuclear weapons is often assumed without considering if doing so will advance their goals or missions. Next, of those that would pursue these weapons, many are limited by a number of strategic and technical constraints. Finally operating under the assumption a terrorist organization is able to obtain a nuclear weapon, this paper shows their options following acquisition are extremely limited and threaten the survivability of their group. A survey of numerous terrorist groups and their capacities find nuclear weapons to be beyond their capabilities. Beyond this assessment, this paper aims to apply a critical lens to the dialogue that often surrounds nuclear terrorism and urges the reader to do the same.