How do climate anomalies affect GDP growth, and how do trade connections help understand this impact? We address these questions exploring local fluctuations in temperature and precipitation coupled with data on supply chain linkages between municipalities in Brazil. GDP growth falls with local anomalous dry spells and to a lower extent, also wet spells. Much of this effect is attributable to moderate levels of climate anomaly. This impact is sufficiently material to transmit across supply chain connections to other municipalities. Focusing on pairs of distant municipalities to avoid common climate shocks, municipalities whose customer firms suffer dry spells have between 1 and 2 percentage points (p.p.) lower GDP growth. This supply chain shock also leads to lower import growth and weaker labour market metrics, suggesting an overall lower level of economic activity. We also examine the major economic sectors separately and find that agricultural activity is more sensitive to supply chain transmission of physical shocks, including moderate ones, than manufacturing (which responds mainly to intense supply chain shocks) or services. This suggests that the local economic mix can be a potentially important driver of effect heterogeneity. Using a counterfactual analysis, we estimate also that supply chain spillovers from climate change varies substantially over the years but can lead to 1 p.p. lower growth on average.