Color–flavor-locked (CFL) quark matter at high densities is a color superconductor, which spontaneously breaks baryon number and chiral symmetry. Its low-energy thermodynamic and transport properties are therefore dominated by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone bosons of which the neutral kaon is the lightest. We study the CFL-K0 phase, in which the stress induced by the strange quark mass causes the kaons to condense, and there is an additional ultra-light ‘K0’ Goldstone boson arising from the spontaneous breaking of isospin. We compute the bulk viscosity of matter in the CFL-K0 phase, which arises from the beta-equilibration processes K0 ↔ H + H and K0 + H ↔ H. We find that the bulk viscosity varies as T7, unlike the CFL phase where it is exponentially Boltzmann suppressed by the kaon's energy gap. However, in the temperature range of relevance for r-mode damping in compact stars, the bulk viscosity in the CFL-K0 phase turns out to be even smaller than in the uncondensed CFL phase, which already has a bulk viscosity much smaller than all other known color-superconducting quark phases.