Abstract Using the non-linear SU(3)L × SU(3)R chiral lagrangian coupled to a field theory of nuclear forces, we show that a bound state of baryons with a well-defined surface may conceivably form in the presence of kaon condensation. This state is of similar density to ordinary nuclei, but has net strangeness equal to about two thirds the baryon number. We discuss the properties of lumps of strange baryon matter with baryon number between ∼ 20 and ∼ 1057 where gravitational effects become important. The possibility that the ground state of baryonic matter at zero pressure is strange and that ordinary nuclei may only be metastable has important consequences for laboratory nuclear physics, the early universe and astrophysical compact objects.