  We present a measurement of the Cabibbo-Kobayashi-Maskawa (CKM) matrix
element |Vcb| using a 10.2 fb^{-1} data sample recorded at the \Upsilon(4S)
resonance with the Belle detector at the KEKB asymmetric e^+e^- storage ring.
By extrapolating the differential decay width of the \bar{B}^0 -->
D^{*+}e^-\bar{\nu} decay to the kinematic limit at which the D^{*+} is at rest
with respect to the \bar{B}^0, we extract the product of |Vcb| with the
normalization of the decay form factor F(1), |Vcb |F(1)=
(3.54+/-0.19+/-0.18)x10^{-2}, where the first error is statistical and the
second is systematic. A value of |Vcb| = (3.88+/-0.21+/-0.20+/-0.19)x10^{-2} is
obtained using a theoretical calculation of F(1), where the third error is due
to the theoretical uncertainty in the value of F(1). The branching fraction
B(\bar{B}^0 --> D^{*+}e^-\bar{\nu}) is measured to be
(4.59+/-0.23+/-0.40)x10^{-2}.
