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Stable bound quantum states are ubiquitous in nature. Mostly, they result from the interaction of only pairs of particles, so called two-body interactions, even when large complex many-particle structures are formed. We show that three-particle bound states occur in a generic, experimentally accessible solid state system: antiferromagnetic spin ladders, related to high-temperature superconductors. This binding is induced by genuine three-particle interactions; without them there is no bound state. We compute the dynamic exchange structure factor required for the experimental detection of the predicted state by resonant inelastic X-ray scattering for realistic material parameters. Our work enables us to quantify these elusive interactions and unambiguously establishes their effect on the dynamics of the quantum many-particle state.