Social norms and the associated altruistic behaviours are decisive for the evolution of human cooperation and the maintenance of social order, and they affect family life, politics and economic interactions. However, as altruistic norm compliance and norm enforcement often emerge in the context of inter-group conflicts, they are likely to be shaped by parochialism--a preference for favouring the members of one's ethnic, racial or language group. We have conducted punishment experiments, which allow 'impartial' observers to punish norm violators, with indigenous groups in Papua New Guinea. Here we show that these experiments confirm the prediction of parochialism. We found that punishers protect ingroup victims--who suffer from a norm violation--much more than they do outgroup victims, regardless of the norm violator's group affiliation. Norm violators also expect that punishers will be lenient if the latter belong to their social group. As a consequence, norm violations occur more often if the punisher and the norm violator belong to the same group. Our results are puzzling for evolutionary multi-level selection theories based on selective group extinction as well as for theories of individual selection; they also indicate the need to explicitly examine the interactions between individuals stemming from different groups in evolutionary models.