A search is performed for a massive new vector-like quark T, with charge 2/3, that is pair produced together with its antiparticle in proton-proton collisions. The data were collected by the CMS experiment at the Large Hadron Collider in 2012 at sqrt(s) = 8 TeV and correspond to an integrated luminosity of 19.5 inverse femtobarns. The T quark is assumed to decay into three different final states, bW, tZ, and tH. The search is carried out using events with at least one isolated lepton. No deviations from standard model expectations are observed, and lower limits are set on the T quark mass at 95% confidence level. The lower limit lies between 687 and 782 GeV for all possible values of the branching fractions into the three different final states assuming strong production. These limits are the most stringent constraints to date on the existence of such a quark.