We compute the bulk viscosity zeta of high-temperature QCD to leading order in powers of the running coupling alpha(s)(T). We find that it is negligible compared to shear viscosity eta for any alpha(s) that might reasonably be considered small. The physics of bulk viscosity in QCD is a bit different than in scalar phi(4) theory. In particular, unlike in scalar theory, we find that an old, crude estimate of zeta similar or equal to 15(1/3-v(s)(2))(2)eta gives the correct order of magnitude, where v(s) is the speed of sound. We also find that leading-log expansions of our result for zeta are not accurate except at very small coupling.