We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisen-berg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z ≈ 1 at the critical temperature, while that of the magne-tization does not measure the performance of the algorithm. This seems to be the first report that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z ≃ 2.