Sr2RuO4 has stood as the leading candidate for a spin-triplet superconductor for 26 years1. However, recent NMR experiments have cast doubt on this candidacy2,3 and it is difficult to find a theory of superconductivity that is consistent with all experiments. The order parameter symmetry for this material therefore remains an open question. Symmetry-based experiments are needed that can rule out broad classes of possible superconducting order parameters. Here, we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr2RuO4 through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus c66, which implies that the superconducting order parameter has two components. A two-component p-wave order parameter, such as px + ipy, naturally satisfies this requirement. As this order parameter appears to have been precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely dxz, dyz and dx2−y2,gxy(x2−y2), are now the prime candidates for the order parameter of Sr2RuO4. © 2020, The Author(s), under exclusive licence to Springer Nature Limited.