Deep chlorophyll maxima (DCMs) are widespread in large parts of the world's oceans. These deep layers of high chlorophyll concentration reflect a compromise of phytoplankton growth exposed to two opposing resource gradients: light supplied from above and nutrients supplied from below. It is often argued that DCMs are stable features. Here we show, however, that reduced vertical mixing can generate oscillations and chaos in phytoplankton biomass and species composition of DCMs. These fluctuations are caused by a difference in the timescales of two processes: (1) rapid export of sinking plankton, withdrawing nutrients from the euphotic zone and (2) a slow upward flux of nutrients fuelling new phytoplankton production. Climate models predict that global warming will reduce vertical mixing in the oceans. Our model indicates that reduced mixing will generate more variability in DCMs, thereby enhancing variability in oceanic primary production and in carbon export into the ocean interior.