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Although experimentally well-established, the nature of the Lambda(1405) hyperon resonance has long been a mystery. Constituent quark models have difficulty accommodating its low mass, while approaches based on chiral effective theory typically predict an additional state, the Lambda(1380), which is broad and difficult to identify. I will present the first lattice QCD computation of the coupled-channel $\pi\Sigma-\bar{K}N$ scattering amplitude in the Lambda(1405) channel, which employs quark masses so that the $\pi\Sigma$ threshold is approximately 1380 MeV. This enables the unambiguous identification of the Lambda(1380) in addition to the Lambda(1405), thus supporting the exotic meson-baryon `molecule' interpretation.