This paper investigates the causal effect of immigration on trade flows using Italian panel data at the province level. We exploit the exceptional characteristics of the Italian data (the fine geographical disaggregation, the very high number of countries of origin of immigrants, the high heterogeneity of social and economic characteristics of Italian provinces, and the absence of cultural or historical ties) coupled with the use of a wide set of fixed effects and an `instrument' based on immigrants' enclaves. We find that immigrants have a significant positive effect on both exports and imports, but much larger for the latter. The pro-trade effects of immigrants tend to decline in space, and even turn negative when large ethnic communities are located too far away from a specific province (via a trade-diversion effect). Moreover, while our data show inter-ethnic spillovers for exports, we find no evidence that networks between different ethnicities affect provinces' imports. Finally, we provide evidence of a substantial heterogeneity in the effects of immigrants: the impact on trade tends to be larger for immigrants coming from low-income countries, for earlier waves of immigrants, and for least advanced provinces (Southern Italy).