Is culture an important variable to explain whether groups can successfully provide public goods? A wealth of empirical evidence on both industrialized and developing countries shows that cooperation levels decrease in the presence of ethnic divisions. Although several laboratory works deal with cultural differences, so far most studies restrict their attention to cross-cultural comparisons among internally homogeneous societies. We depart from these contributions and conduct an intercultural public goods game with punishment experiment in Italy, a country where immigration is a quite recent, but politically hot phenomenon. We investigate the effects of introducing a varying number of foreign participants within a homogeneous pool of native subjects. Our results indicate that foreigners contribute significantly less than natives, natives react lowering their own contribution levels, and, consequently, the degree of cultural diversity negatively affects the overall level of cooperation. In terms of sanctioning, we observe no difference in the overall amount of assigned and received punishment points; however, behaving mostly as free-riders, foreigners are more likely to use anti-social punishment. In the absence of institutional restrictions ruling out anti-social punishment, this might amplify the documented detrimental effect on cooperation.