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.
