A measurement of the fraction, f⁺, of right-handed W bosons produced in top quark decays is presented. This analysis is based on a sample corresponding to an integrated luminosity of 370 pb⁻¹, collected by the D⊘ detector at the Fermilab Tevatron pp Collider at √s = 1.96 TeV. The helicity angle, θ*, is reconstructed for each lepton. f⁺ is determined by comparing the cos θ* distribution from the data with that for the expected background and signal for various values of f⁺. The fraction of longitudinal W bosons, f⁰, is assumed to be 0.7 as predicted by the standard model. This yields f⁺ = 0.109 ± 0.094 (stat) ± 0.063 (syst), consistent with the standard model prediction of f⁺ = 3.6× 10⁻⁴. The possibility that both f⁺ and f⁰ stray from standard model values is also investigated. In this case cos θ* distributions for each possible W helicity state, along with the backgrounds, are fit to the cos θ* distribution for the data. The best fit values are f⁺ = 0.82 ± 0.30(stat) and f⁰ = −0.58 ± 0.50(stat).