  The neutron spin rotation induced by parity-violating (PV) components in the
nucleon-nucleon potential is studied in \vec{n}-d scattering at zero energy.
Results are obtained corresponding to the Argonne v_{18} two-nucleon and
Urbana-IX three-nucleon strong-interaction potentials in combination with
either the DDH or pionless EFT model for the weak-interaction potential. We
find that this observable is dominated by the contribution of the long-range
part of the PV potential associated with pion exchange. Thus its measurement
could provide a further constraint, complementary to that coming from
measurements of the photon asymmetry in \vec{n}-p radiative capture, on the
strength of this component of the hadronic weak interaction.
