Peace and global security are human endeavors, and thus their attainment depends as much on psychology as it does on governance and technology. In this paper I outline 3 ways our evolved psychology is an obstacle to achieving international cooperation and peace. First, humans show strong evidence of adaptations for cooperation within groups, but equally clear evidence that this cooperative nature does not extend to members of other groups. Second, humans evolved to have a relative sense of fairness, and thus will often reject even mutually beneficial agreements if they benefit others more than themselves. Third, humans evolved to be self-deceptive and hypocritical, believing in the unique righteousness and inevitable victory of their own cause, which tends to exacerbate conflict. Nevertheless, these obstacles are not insurmountable and an awareness of them can help in the development of strategies to increase the chances of lasting peace and security.