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Kaon and antikaon production and antikaon condensation in neutron star matter are investigated in a chiral hadronic model proposed by Furnstahl, Tang, & Serot (FST model). Results calculated in the FST model are compared with those in the nonlinear Walecka model. Antikaon condensation decreases the maximum masses of neutron stars with a composition of (n, p, e, m, K) compared with those of (n, p, e, m), without antikaon condensation. The FST model predicts that S+ and Ks0 do not occur in neutron stars. Moreover, it has been shown that antikaon condensation in the FST model does not exist in neutron star matter with compositions of both (n, p, e, m, K, H) if hyperons are considered and (n, p, e, m, ne, K, H) if hyperons plus neutrino tripping are considered. The Q-values for K+ and K- production are not sensitive to antikaon condensation and the presence of hyperons. In-medium effects decrease the Q-values for NN - NNK+K- and LN - NNK- and increase those for NN - NLK+, K-p - Lp0, and K-n - Lp- as the density of neutron star matter increases.