A search is presented in proton-proton collisions at sqrt(s) = 7 TeV for fermionic triplet states expected in type III seesaw models. The search is performed using final states with three isolated charged leptons and an imbalance in transverse momentum. The data, collected with the CMS detector at the LHC, correspond to an integrated luminosity of 4.9 inverse femtobarns. No excess of events is observed above the background predicted by the standard model, and the results are interpreted in terms of limits on production cross sections and masses of the heavy partners of the neutrinos in type III seesaw models. Depending on the considered scenarios, lower limits are obtained on the mass of the heavy partner of the neutrino that range from 180 to 210 GeV. These are the first limits on the production of type III seesaw fermionic triplet states reported by an experiment at the LHC.