We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen–Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the “energy-like” observables, we find z int, N =z int, E =z int, E′ =0.459±0.005±0.025 , where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the “susceptibility-like” observables, we find z int, M 2 =z int, S 2 =0.443±0.005±0.030 . For the dynamic critical exponent associated to the exponential autocorrelation time, we find z exp≈0.481. Our data are consistent with the Coddington–Baillie conjecture z SW= β/ ν≈0.5183, especially if it is interpreted as referring to z exp.