In the standard model, the charged current of the weak interaction is governed by a unitary quark mixing matrix that also leads to CP violation. Measurement of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements is essential to searches for new physics, either through the structure of the CKM matrix, or a departure from unitarity. We determine the CKM matrix element |V cb| using a sample of 3×10 6 BB̄ events in the CLEO detector at the Cornell Electron Storage Ring. We determine the yield of reconstructed B̄ 0 →D* + ℓν̄ and B -D* 0ℓν̄ decays as a function of w, the boost of the D* in the B rest frame, and from this we obtain the differential decay rate dΓ/dw. By extrapolating dΓ/dw to w = 1, the kinematic end point at which the D* is at rest relative to the B, we extract the product |V cb|ℱ(1), where ℱ(1) is the form factor at w=1. We find |V cb|ℱ(1) = 0.0431±0.0013(stat) ±0.0018(syst). We combine |V cb|ℱ(1) with theoretical results for ℱ(1) to determine |V cb| = 0.0469±0.0014(stat) ±0.0020(syst)±0.0018(theor). We also integrate the differential decay rate over w to obtain B(B̄ 0→D * +ℓν̄ = (609±0.19±0.40)% and B(B -→D* 0ℓν̄) = (6.50±0. 20±0.43)%.