We report on a search for the flavor-changing neutral current
decays B+ --> mu+ mu- K+ and B0 --> mu+ mu- K*0 using 88 pb-1 of data
from p anti-p collisions at s**(1/2) = 1.8 TeV, collected with the Collider
Detector at Fermilab. Finding no evidence for these decays, we set upper
limits on the branching fractions B(B+ --> mu+ mu- K+)