We present a search for a narrow resonance in the tbbar mass spectrum using 1.9 fb−1 of ppbar collisions at sqrt(s) = 1.96 TeV recorded with the CDF II detector at the Fermilab Tevatron. We select events with a lepton, neutrino candidate, and two or three jets from which to construct the tbbar mass. We quantify the result using the model of a massive Standard Model-like charged-boson (W;;) decaying to tbbar, but we are generally sensitive to the presence of any narrow state decaying to the third generation. For a purely right-handed W;; with Standard Model couplings, we set a new limit at 95% confidence of sigma(ppbar -> W;;) x BR(W;; -> tbbar) < 0.28 pb and M_W;; > 800 GeV/c2. The limit increases to M_W;; > 825 GeV/c2 if decay to right-handed neutrinos is forbidden. For a right-handed W;; (or left-handed W;; with negligible interference) with arbitrary coupling strength, we set limits on that coupling as a function of W;; mass between 300 to 950 GeV/c^2.