This work assesses the changes in power capacity expansion decisions regarding power generation and transmission that occur when the effects of Climate Change on wind speed are captured in the decision model. Considering an 85-year period (2016–2101), we use a Mixed-Integer Linear Program (MILP) model to analyze the optimal power capacity expansion in diverse types of power generation technologies, throughout the years and geographical locations. The optimization model minimizes the total (investment and operational) costs of the power system subject to several technical and economic constraints. We implement our model using the main Chilean power system. We compare two scenarios: one assuming that Climate Change affects wind speeds and hence wind farm capacity factors and the other assuming it does not. Our results reveal that, when taking into account the impact of Climate Change on wind speed, the optimal power generation and transmission expansion plan is different than when ignoring this effect. The variation of wind speed affects not only wind power capacity installed, but also other-technology power capacity installed. In particular, power capacity installed in wind and solar generation plants is higher (measured in MW installed) than the power capacity installed when we ignore the effects of Climate Change; and power capacity installed in diesel and natural gas technologies are lower. We perform sensitivity analyses, changing power capacity expansion limits and the discount rate, to check for the robustness of our results.