  Chiral effective field theory (EFT) provides a systematic expansion for the
coupling of WIMPs to nucleons at the momentum transfers relevant to direct cold
dark matter detection. We derive the currents for spin-dependent WIMP
scattering off nuclei at the one-body level and include the leading long-range
two-body currents, which are predicted in chiral EFT. As an application, we
calculate the structure factor for spin-dependent WIMP scattering off 129,131Xe
nuclei, using nuclear interactions that have been developed to study nuclear
structure and double-beta decays in this region. We provide theoretical error
bands due to the nuclear uncertainties of WIMP currents in nuclei.
