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This Letter describes the search for a new heavy charged gauge boson W′ decaying into an electron and a neutrino. The data were collected with the D0 detector at the Fermilab Tevatron pp̅ Collider at √s = 1.96 TeV, and correspond to an integrated luminosity of about 1 fb-1. Lacking any significant excess in the data in comparison with known processes, an upper limit is set on σW′ x B(W′ → eν) and a W′ boson with mass below 1.00 TeV can be excluded at the 95% C.L., assuming standard-model-like couplings to fermions. This result significantly improves upon previous limits and is the most stringent to date.