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We analyze the presence of nonreciprocal critical currents, the so-called superconducting diode effect, in chiral superconductors within a generalized Ginzburg-Landau framework. After deriving its key symmetry conditions we illustrate the basic mechanism for two examples, the critical current in a thin film and a Josephson junction. The appearance of spontaneous edge currents and the energy bias for the formation of Josephson vortices play an essential part in establishing a splitting of the critical currents running in opposite directions. Eventually this allows us to interpret a superconducting diode effect observed in the 3-Kelvin phase of Sr_{2}RuO_{4} as evidence for spontaneously broken time-reversal symmetry in the superconducting phase.