Results are presented from a search for the rare decays B-s(0) -> mu(+) mu(-) and B-0 -> mu(+) mu(-) in pp collisions at root 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(B-s(0) -> mu(+)mu(-)) = (3.0(-0.9)(+1.0)) x 10(-9), where the uncertainty includes both statistical and systematic contributions. An excess of B-s(0) -> mu(+)mu(-) events with respect to background is observed with a significance of 4.3 standard deviations. For the decay B-0 -> mu(+)mu(-) an upper limit of 'B(B-0 -> mu(+) mu(-)) < 1.1 x 10(-9) at the 95% confidence level is determined. Both results are in agreement with the expectations from the standard model.