Using the Collider Detector at Fermilab, the W boson differential cross section (d sigma)/(d Pt), is measured using W --> e nu events in proton-antiproton collisions at s**(1/2) = 1.8 TeV. A next-to-leading order theoretical calculation agrees well withthe data. The crossection (sigma) for Pt > 50 GeV/(c**2) is measured to be 423+-58(stat.)+-108(sys.) pb.