The chemical sector is confronted with risks pertaining to accidents involving dangerous substances. At the European level, a set of regulations - the Seveso regime - aims at controlling such risks. This article explores how this regime is put into practice, by analyzing the local practices of enforcement by Dutch inspectors and compliance by Dutch chemical companies. These empirical insights demonstrate that the classical 'positivistic risk paradigm' - which treats all risks as calculable, controllable and reducible seems to dominate in the Seveso regime. The analysis in this article shows that this can lead to 'uncertainty blindness': a regulatory regime where only yesterday's accidents are managed and salient future risks are potentially overlooked. We suggest that both regulators and regulated should start accepting the possibility of uncertain risks, which implies a cultural change in the current regulatory regime to 'uncertainty tolerance'.