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An effective chiral Lagrangian in heavy-fermion formalism whose parameters are constrained by kaon-nucleon and kaon-nuclear interactions next to the leading order in chiral expansion is used to describe kaon condensation in dense "neutron star" matter. The critical density is found to be robust with respect to the parameters of the chiral Lagrangian and comes out to be ρ c ∼ (3 − 4)ρ 0 . Once kaon condensation sets in, the system is no longer composed of neutron matter but of nuclear matter. Possible consequences on stellar collapse with the formation of compact "nuclear stars" or light-mass black holes are pointed out.