Evidence is presented for the associated production of a single top quark and W boson in pp collisions at sqrt[s]=7 TeV with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 4.9 fb(-1). The measurement is performed using events with two leptons and a jet originated from a b quark. A multivariate analysis based on kinematic properties is utilized to separate the tt background from the signal. The observed signal has a significance of 4.0σ and corresponds to a cross section of 16(-4)(+5) pb, in agreement with the standard model expectation of 15.6±0.4(-1.2)(+1.0) pb.