We report results from Experiment 871, performed at the BNL AGS, of a measu
rement of the branching ratio K-L(0) --> mu(+)mu(-) with respect to the CP-
violating mode K-L(0) --> pi(+)pi(-). This experiment detected over 6200 ca
ndidate mu(+)mu(-) events, a factor of 6 more than that seen in all previou
s measurements combined. The resulting branching ratio Gamma(K-L(0) --> mu(
+)mu(-))/Gamma(K-L(0) --> pi(+)pi(-)) = (3.474 +/- 0.057) X 10(-6) leads to
a branching fraction B(K-L(0) --> mu(+)mu(-)) = (7.18 +/- 0.17) X 10(-9),
which is consistent with the current world average, and reduces the uncerta
inty in this decay mode by a factor of 3.