We have developed a new technique for inclusive reconstruction of the energy of B hadrons. The excellent efficiency and resolution of this technique allow us to make the most precise determination of the b-quark fragmentation function, using e(+)e(-)-->Z0 decays recorded in the SLAC Large Detector experiment. We compared our measurement with the predictions of a number of fragmentation models. We excluded several of these models and measured the average scaled energy of weakly decaying B hadrons to be <x(B)> = 0.714+/-0. 005(stat)+/-0.007(syst)+/-0.002 (model dependence).