  We investigate the shear viscosity of neutron star matter in the presence of
an antikaon condensate. The electron and muon number densities are reduced due
to the appearance of a $K^-$ condensate in neutron star matter, whereas the
proton number density increases. Consequently the shear viscosity due to
scatterings of electrons and muons with themselves and protons is lowered
compared to the case without the condensate. On the other hand, the
contribution of proton-proton collisions to the proton shear viscosity through
electromagnetic and strong interactions, becomes important and comparable to
the neutron shear viscosity.
