Recent experiments suggest that Sr2RuO4 has a two-component superconducting order parameter (OP). A two-component OP has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls-a possibility that would explain a number of experimental observations including the smallness of the signature of time reversal symmetry breaking at Tc and telegraph noise in critical current experiments. We use resonant ultrasound spectroscopy to perform ultrasound attenuation measurements across the superconducting Tc of Sr2RuO4. We find that compressional sound attenuation increases by a factor of 7 immediately below Tc, in sharp contrast with what is found in both conventional (s-wave) and high-Tc (d-wave) superconductors. Our observations are most consistent with the presence of domain walls that separate different configurations of the superconducting OP. The fact that we only observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally degenerate superconducting OPs that are not related to each other by symmetry. Whatever the mechanism, a factor of 7 increase in sound attenuation is a singular characteristic that must be reconciled with any potential theory of superconductivity in Sr2RuO4. © 2022 American Physical Society.