  We investigate the contribution of zero-point motion, arising from
fluctuations in kaon modes, to the ground state properties of neutron star
matter containing a Bose condensate of kaons. The zero-point energy is derived
via the thermodynamic partition function, by integrating out fluctuations for
an arbitrary value of the condensate field. It is shown that the vacuum
counterterms of the chiral Lagrangian ensure the cancellation of divergences
dependent on $\mu$, the charge chemical potential, which may be regarded as an
external vector potential. The total grand potential, consisting of the
tree-level potential, the zero-point contribution, and the counterterm
potential, is extremized to yield a locally charge neutral, beta-equilibrated
and minimum energy ground state. In some regions of parameter space we
encounter the well-known problem of a complex effective potential. Where the
potential is real and solutions can be obtained, the contributions from
fluctuations are found to be small in comparison with tree-level contributions.
