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+ --&gt; mu+ mu- K+) <lt; 5.2 x 10-6 and
B(B0 --&gt; mu+ mu- K*0) <lt; 4.0 x 10-6 at the 90% confidence level.