  We report on a search for Bs->mu+mu- and Bd->mu+mu- decays in ppbar
collisions at sqrt(s)=1.96 TeV using 171 pb-1 of data collected by the CDF II
experiment at the Fermilab Tevatron Collider. The decay rates of these rare
processes are sensitive to contributions from physics beyond the Standard
Model. One event survives all our selection requirements,consistent with the
background expectation. We derive branching ratio limits of BR(Bs->mu+mu-) <
5.8 x 10^-7 and BR(Bd->mu+mu-) < 1.5 x 10^-7 at 90% confidence level.
