  We investigate the existence of bound states of baryons in a kaon condensate
using chiral mean field theory.
  The interactions are described by an effective SU(3)_L X SU(3)_R chiral
lagrangian where terms of higher order in density, baryon momentum, and kaon
mass are suppressed by powers of the symmetry breaking scale, Lambda. We take
up to next to leading order terms (n = 2,3,4). We search for infinite baryon
number solutions, namely ``strange baryonic matter'', using a Thomas-Fermi
approximation for a slowly varying condensate and a lowest order Hartree
approximation to describe the many body interactions. For simplicity we study a
pure K^0 condensate and only neutrons, the lightest baryons in that condensate.
We find solutions with neutron number densities, rho_n > 3.5 rho_0, where rho_0
is the infinite nuclear matter density. This is consistent with the estimate of
the onset of a K-condensate at rho_n = 2-4 rho_0. We show that the binding
energies, E_b, grow with rho_n and for rho_n < 7 rho_0 (at rho_n > 7 rho_0
perturbative expansion is lost) we find E_b < 150 MeV (E_b < 70 MeV for rho_n <
5 rho_0) even in the most favorable cases. These binding energies may be too
low for this type of matter to appear and persist in the early universe.
