  We apply the event-chain Monte Carlo algorithm to the three-dimensional
ferromagnetic Heisenberg 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 $z \approx 1$ at the critical
temperature, while that of the magnetization 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 $z\simeq 2$.
