We report on a search for B0(s) --> mu+ mu- and B0(d) --> mu+
mu- decays in p anti-p collisions at s**(1/2) = 1.96 TeV using 364 pb-1 of data
collected by the CDF II detector at the Fermilab Tevatron Collider. After
applying all selection requirements, we observe no candidates inside the
B0(s) and B0(d) mass windows, consistent with the background expectation.
The resulting upper limits on the branching fractions are B(B0(s) --> mu+
mu-) < 1.5 x 10-7 and B(B0(d) --> mu+ mu-) < 3.9 x 10-8 at 90%
confidence level.