This article is a radical rethinking of public international law through the use of Lacanian psychoanalysis. Its central thesis is that while contemporary scholarship addresses what Lacan calls the symbolic and imaginary registers including law, politics, and ideology, it continues to ignore and repress the dimension of the real. The article illustrates this with a clinical example examined by Kris and discussed by Lacan. Imagining public international law as an indefatigable neurotic in search of ‘fresh brains’, the article shows why meeting her in the domains of law and politics is not enough to satiate her appetite. What continues to resist is the ‘extimate’, the inhuman element within the human that the subject hides so well from herself that it is excluded in the interior. A major instance of the extimate is the ‘caffeinated neighbour’, that is, the neighbour who is not in our image because her disturbing core has not been subtracted. The article argues that unless international law comes to terms with this inevitably ugly and obscene core, in oneself as well as in the neighbour, it cannot hope to achieve any meaningful changes. That the need to recognize the extimate is the ethical demand facing international law now; unless we address it, our symptoms will continue to grow and we will continue to crave fresh brains.