We use the transverse momentum spectrum of leptons in the decay chain t --> bW with W --> l nu to measure the helicity of the W bosons in the top quark rest frame. Ourmeasurement uses a tt sample isolated in 106 +/- 4 pb(-1) of data collected in <p(p)over bar> collisions at root s = 1.8 TeV with the CDF detector at the Fermilab Tevatron. Assuming a standard. V-A weak decay, we find that the fraction of W's with zero helicity in the top rest frame is F-0 = 0.91 +/- 0.37(stat) +/- 0.13(syst), consistent with the standard model prediction of F-0 = 0.70 for a top mass of 175 GeV/c(2). RI Lancaster, Mark/C-1693-2008; Vucinic, Dejan/C-2406-2008; Nomerotski, Andrei/A-5169-2010; Prokoshin, Fedor/E-2795-2012; Chiarelli, Giorgio/E-8953-2012; Azzi, Patrizia/H-5404-2012