Between 1992 and 2018, the breeding population of Adélie penguins around Anvers Island, Antarctica declined by 98%. In this region, natural climate variability drives five‐year cycling in marine phytoplankton productivity, leading to phase‐offset five‐year cycling in the size of the krill population. We demonstrate that the rate of change of the Adélie breeding population also shows five‐year cycling. We link this population response to cyclical krill scarcity, a phenomenon which appears to have arisen from the interaction between climate variability and climate change trends. Modeling suggests that, since at least 1980, natural climate variability has driven cycling in this marine system. However, anthropogenic climate change has shifted conditions so that fewer years in each cycle now prompt strong krill recruitment, triggering intervals of krill scarcity that result in drastic declines in Adélie penguins. Our results imply that climate change can amplify the impacts of natural climate oscillations across trophic levels, driving cycling across species and disrupting food webs. The findings indicate that climate variability plays an integral role in driving ecosystem dynamics under climate change.