The rich multiparticle dynamics of QCD, which includes resonances and bound states, leaves an imprint on the spectrum of the theory confined to a finite volume. Turning this relationship around, scattering amplitudes can be constrained through precise measurements of the small energy shifts due to the interaction, which are accessible in first-principle lattice QCD simulations. For the first time we have computed the spectrum of three positively charged pions in several symmetry sectors of the finite volume, enabling a peek at three-particle dynamics directly from QCD.