  Using 14M psi(2S) events taken with the BES-II detector, chi_cJ-->K+K-K+K-
decays are studied. For the four-kaon final state, the branching fractions are
B(chi_c0,1,2 -->K+K-K+K-)=(3.48\pm 0.23\pm 0.47)\times 10^{-3}, (0.70\pm
0.13\pm 0.10)\times 10^{-3}, and (2.17\pm 0.20\pm 0.31)\times 10^{-3}. For the
\phi K+K- final state, the branching fractions, which are measured for the
first time, are B(chi_c0,1,2-->\phi K+K-)=(1.03\pm 0.22\pm 0.15)\times 10^{-3},
(0.46\pm 0.16\pm 0.06)\times 10^{-3}, and (1.67\pm 0.26\pm 0.24)\times 10^{-4}.
For the \phi\phi final state, B(chi_{c0,2}-->\phi\phi)=(0.94\pm 0.21\pm
0.13)\times 10^{-3} and (1.70\pm 0.30\pm 0.25)\times 10^{-3}.
