A study of b quark fragmentation at LEP is presented using a sample of semileptonic B decays containing a fully reconstructed charm meson. The data are compared to several theoretical models for heavy quark fragmentation; the free parameters in these models are fitted and the sensitivity of the model parameters to the rate of P-wave B meson production is studied. The mean scaled energy fraction of B 0 and B + mesons has been determined to be <x E > = 0.695 +/- 0.006 +/- 0.003 +/- 0.007, where the errors are statistical, systematic and model dependence respectively. This result is consistent with previous, less direct measurements from inclusive leptonic B decays. Also presented is a model independent fit to the shape of the energy distribution of weakly decaying B mesons at LEP.