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 BB events in the CLEO detector at the Cornell Electron Storage Ring. We determine the yield of reconstructedB 0 → D * + ℓν and B − → D * 0 ℓν 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(theo.). We also integrate the differential decay rate over w to obtain B(B 0 → D * + ℓν) = (6.09 ± 0.19 ± 0.40)% and B(B − → D * 0 ℓν) = (6.50 ± 0.20 ± 0.43)%.2