Results are presented from a search for the rare decays Bs(0)→μ+ μ- and B(0)→μ+ μ- in pp collisions at sqrt[s]=7 and 8 TeV, with data samples corresponding to integrated luminosities of 5 and 20 fb(-1), respectively, collected by the CMS experiment at the LHC. An unbinned maximum-likelihood fit to the dimuon invariant mass distribution gives a branching fraction B(Bs(0)→μ+ μ-)=(3.0(-0.9)(+1.0))×10(-9), where the uncertainty includes both statistical and systematic contributions. An excess of Bs(0)→μ+ μ- events with respect to background is observed with a significance of 4.3 standard deviations. For the decay B(0)→μ+ μ- an upper limit of B(B(0)→μ+ μ-)<1.1×10(-9) at the 95% confidence level is determined. Both results are in agreement with the expectations from the standard model.