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Centrioles are barrel-shaped structures that duplicate when a mother centriole gives birth to a single daughter that grows from its side. Polo-like-kinase 4 (PLK4), the master regulator of centriole biogenesis, is initially recruited around the mother centriole, but it rapidly breaks symmetry to concentrate at a single focus that defines the daughter centriole assembly site. Two previous studies used different molecular and mathematical models to simulate PLK4 symmetry breaking. Here, we extract the core biological principles from both models to formulate a new and conceptually-simple mathematical model in which phosphorylated and unphosphorylated species of PLK4 (either on their own, or in complexes with other centriole duplication proteins) form the two-components of a classic Turing reaction-diffusion system. These two components bind/unbind from the mother centriole at different rates, and so effectively diffuse around the mother at different rates. This allows a slow-diffusing “activator” species to accumulate at a single site on the mother, while a fast-diffusing “inhibitor” species rapidly diffuses around the rest of the centriole to suppress activator accumulation. We conclude that phosphorylated and unphosphorylated species of PLK4 can form a Turing reaction-diffusion system, allowing PLK4 to break symmetry and generate a single daughter centriole.