  We present a measurement of the fractions F_0 and F_+ of longitudinally
polarized and right-handed W bosons in top quark decays using data collected
with the CDF II detector. The data set used in the analysis corresponds to an
integrated luminosity of approximately 318 pb -1. We select ttbar candidate
events with one lepton, at least four jets, and missing transverse energy. Our
helicity measurement uses the decay angle theta*, which is defined as the angle
between the momentum of the charged lepton in the W boson rest frame and the W
momentum in the top quark rest frame. The cos(theta*) distribution in the data
is determined by full kinematic reconstruction of the ttbar candidates. We find
F_0 = 0.85 +0.15 -0.22 (stat) +- 0.06 (syst) and F_+ = 0.05 +0.11 -0.05 (stat)
+- 0.03 (syst), which is consistent with the standard model prediction. We set
an upper limit on the fraction of right-handed W bosons of F_+ < 0.26 at the
95% confidence level.
