Resonant hadronic systems often exhibit a complicated decay pattern in which three-body dynamics play a relevant or even dominant role. In this work we focus on the a_{1}(1260) resonance. For the first time, the pole position and branching ratios of a three-body resonance are calculated from lattice QCD using one-, two-, and three-meson interpolators and a three-body finite-volume formalism extended to spin and coupled channels. This marks a new milestone for ab initio studies of ordinary resonances along with hybrid and exotic hadrons involving three-body dynamics.