We report on a search for the decay K-L --> pi(0)mu(+)mu(-) carried out as
a part of the KTeV experiment at Fermilab. This decay is expected to have a
significant CP violating contribution and a direct measurement will either
support the Cabibbo-Kobayashi-Maskawa mechanism for CP violation or point
to new physics. Two events were observed in the 1997 data with an expected
background of 0.87 +/- 0.15 events, and we set an upper limit B (K-L --> pi
(0)mu(+)mu(-)) < 3.8 X 10(-10) at the 90% confidence level.