The causal efficacy of a material system is usually thought to be produced by the law-like actions and interactions of its constituents. Here, a specific system is constructed and explained that produces a cause that cannot be understood in this way, but instead has novel and autonomous efficacy. The construction establishes a proof-of-feasibility of strong emergence. The system works by utilizing randomness in a targeted and cyclical way, and by relying on sustained evolution by natural selection. It is not vulnerable to standard arguments against strong emergence, in particular ones that assume that the physical realm is causally closed. Moreover, it does not suffer from epiphenomenalism or causal overdetermination. The system uses only standard material components and processes, and is fully consistent with naturalism. It is discussed whether the emergent cause can still be viewed as ‘material’ in the way that term is commonly understood.