We present a measurement of the W boson mass using 200/pb of data collected in pbar p collisions at sqrt(s) = 1.96 TeV by the CDF II detector at Run II of the Fermilab Tevatron. With a sample of 63964 W -> e nu candidates and 51128 W -> mu nu candidates, we measure M_W = (80413 +- 34 (stat) +- 34 (syst) = 80413 +- 48) MeV/c^2. This is the most precise single measurement of the W boson mass to date.

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