Can we reduce the damage from climate change by investing in seawalls, stilts, or other forms of adaptation? Focusing on the case of severe storms in the US, I develop a macro heterogeneous-agent model to quantify the interactions between adaptation, federal disaster policy, and climate change. The model departs from the standard climate damage function and incorporates the damage from storms as the realization of idiosyncratic shocks. Using the calibrated model, I infer that adaptation capital comprises approximately one percent of the US capital stock. I find that while the moral hazard effects from disaster aid reduce adaptation in the US economy, federal subsidies for investment in adaptation more than correct for the moral hazard. I introduce climate change into the model as a permanent increase in either or both the severity or probability of storms. Adaptation reduces the damage from this climate change by approximately one third. Finally, I show that modeling the idiosyncratic risk component of climate damage has quantitatively important implications for adaptation and for the welfare cost of climate change.