  A search has been performed for B_s --> mu+mu- and B_d --> mu+mu- decays
using 7/fb of integrated luminosity collected by the CDF II detector at the
Fermilab Tevatron collider. The observed number of B_d candidates is consistent
with background-only expectations and yields an upper limit on the branching
fraction of BF(B_d-->mu+mu-) < 6.0E-9 at 95% confidence level. We observe an
excess of B_s candidates. The probability that the background processes alone
could produce such an excess or larger is 0.27%. The probability that the
combination of background and the expected standard model rate of B_s -->
mu+mu- could produce such an excess or larger is 1.9%. These data are used to
determine BF(B_s-->mu+mu-) = (1.8^{+1.1}_{-0.9})E-8 and provide an upper limit
of BF(B_s -->mu+mu-) < 4.0E-8 at 95% confidence level.
