The dynamics of the Peru–Chile upwelling system (PCUS) are primarily driven by alongshore wind stress and curl, like in other eastern boundary upwelling systems. Previous studies have suggested that upwelling-favorable winds would increase under climate change, due to an enhancement of the thermally-driven cross-shore pressure gradient. Using an atmospheric model on a stretched grid with increased horizontal resolution in the PCUS, a dynamical downscaling of climate scenarios from a global coupled general circulation model (CGCM) is performed to investigate the processes leading to sea-surface wind changes. Downscaled winds associated with present climate show reasonably good agreement with climatological observations. Downscaled winds under climate change show a strengthening off central Chile south of 35°S (at 30°S–35°S) in austral summer (winter) and a weakening elsewhere. An alongshore momentum balance shows that the wind slowdown (strengthening) off Peru and northern Chile (off central Chile) is associated with a decrease (an increase) in the alongshore pressure gradient. Whereas the strengthening off Chile is likely due to the poleward displacement and intensification of the South Pacific Anticyclone, the slowdown off Peru may be associated with increased precipitation over the tropics and associated convective anomalies, as suggested by a vorticity budget analysis. On the other hand, an increase in the land–sea temperature difference is not found to drive similar changes in the cross-shore pressure gradient. Results from another atmospheric model with distinct CGCM forcing and climate scenarios suggest that projected wind changes off Peru are sensitive to concurrent changes in sea surface temperature and rainfall.