Kaon condensation in hyperon-mixed matter [(Y+K) phase], which may be realized in neutron stars, is discussed on the basis of chiral symmetry. With use of the effective chiral Lagrangian for kaon (K)-baryon (B) and K-K interactions, coupled with the relativistic mean-field theory and universal three-baryon repulsive interaction, we clarify the effects of the s-wave K-B scalar interaction simulated by the K-B sigma terms and vector interaction (Tomozawa-Weinberg term) on kaon properties in hyperon-mixed matter, onset density of kaon condensation, and the EOS with the (Y+K) phase. In particular, the quark condensates in the (Y+K) phase are obtained, and their relevance to chiral symmetry restoration is discussed.