We describe a measurement of the W boson mass m_w using 200
pb-1 of s**(1/2) = 1.96 TeV p anti-p collision data taken with the CDF
II detector. With a sample of 63, 964 W --> e nu candidates and 51,128
W --> mu nu candidates, we measure m_w = [80.413 +/- 0.034(stat) +/-
0.034(sys) = 80.413 +/- 0.048] GeV/c2. This is the single most precise
m_w measurement to date. When combined with other measured electroweak
parameters, this result further constrains the properties of new observed
particles coupling to W and Z bosons.