Centriole function has been difficult to study because of a lack of specific tools that allow persistent and reversible centriole depletion. Here we combined gene targeting with an auxin-inducible degradation system to achieve rapid, titratable, and reversible control of Polo-like kinase 4 (Plk4), a master regulator of centriole biogenesis. Depletion of Plk4 led to a failure of centriole duplication that produced an irreversible cell cycle arrest within a few divisions. This arrest was not a result of a prolonged mitosis, chromosome segregation errors, or cytokinesis failure. Depleting p53 allowed cells that fail centriole duplication to proliferate indefinitely. Washout of auxin and restoration of endogenous Plk4 levels in cells that lack centrioles led to the penetrant formation of de novo centrioles that gained the ability to organize microtubules and duplicate. In summary, we uncover a p53-dependent surveillance mechanism that protects against genome instability by preventing cell growth after centriole duplication failure.