The decay chain b -> .hivin.B -> D**0l-nX, D**0 -> D*+p-, D0p+, D0 -> (Kp or K3p) is identified in a sample of 3.9 million hadronic Z decays collected with the OPAL detector at LEP. The branching ratio BR(b -> .hivin.B) x BR (.hivin.B -> D01l-nX) x BR(D01 -> D*+p-) is measured to be (2.64 +- 0.79(stat)+-0.39(syst)) x 10-3 for the JP=1+ (D01) state. For decays into the JP=2+ (D*01) state, an upper limit of 1.4 x 10-3 is placed on the branching ratio at the 95% confidence level. [on SciFinder (R)]