We present a search for a narrow-width heavy resonance decaying into top quark pairs (X→tt¯) in pp¯ collisions at s=1.96TeV using approximately 0.9fb−1 of data collected with the DØ detector at the Fermilab Tevatron Collider. This analysis considers tt¯ candidate events in the lepton plus jets channel with at least one identified b jet and uses the tt¯ invariant mass distribution to search for evidence of resonant production. We find no evidence for a narrow resonance X decaying to tt¯. Therefore, we set upper limits on σX⋅B(X→tt¯) for different hypothesized resonance masses using a Bayesian approach. For a Topcolor-assisted technicolor model, the existence of a leptophobic Z′ boson with mass MZ′<700GeV and width ΓZ′=0.012MZ′ can be excluded at the 95% C.L.