This paper explores the role of social norms in influencing the incidence of sexual assault, and the contribution of alcohol to such events. We build a decision theoretic model where agents may choose to use alcohol as a ``disinhibitor" to undermine social norms discouraging consensual sexual encounters outside marriage. This has the side-effect of making non-consensual encounters more likely. By making the resort to alcohol more attractive, stronger norms against consensual sex may increase the overall incidence of non-consensual sex. We test this theory on data from US college campuses: colleges located in counties without Planned Parenthood clinics, as well as those with a religious affiliation, have more incidents of rape and sexual assault in which alcohol is implicated, and more incidents in total. We explore rival explanations such as reporting and selection biases. Estimates on a restricted sub-sample for which attitudinal data are available show a significant association of assault with the proportion of students expressing strong disapproval of consensual pre-marital sex; this seems to be the main reason for the higher incidence on religiously-affiliated campuses. Restrictions on availability of alcohol substantially reduce the frequency of such incidents. All else equal, the average variation between secular and religious campuses in the incidence of assaults with alcohol is two to three times higher than the variation on any particular campus between weekdays and weekends.