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Strontium ruthenate (Sr2RuO4) continues to present an important test of our understanding of unconventional superconductivity, because while its normal-state electronic structure is known with precision, its superconductivity remains unexplained. There is evidence that its order parameter is chiral, but reconciling this with recent observations of the spin part of the pairing requires an order parameter that is either finely tuned or implies a new form of pairing. Therefore, a definitive resolution of whether the superconductivity of Sr2RuO4is chiral is important for the study of superconductivity. Here we report the measurement of zero-field muon spin relaxation—a probe sensitive to weak magnetism—on samples under uniaxial stresses. We observe stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking—consistent with the qualitative expectations for a chiral order parameter—and argue that this observation cannot be explained by conventional magnetism. In addition, we report the appearance of bulk magnetic order under higher uniaxial stress, above the critical pressure at which a Lifshitz transition occurs in Sr2RuO4.