The decays Upsilon(4S) -> BB, followed by B -> D* pi and D* -> D pi, permit reconstruction of all kinematic quantities that describe the sequence without reconstruction of the D, with reasonably low backgrounds. Using an integrated e+e- luminosity of 3.1 fb^{-1} accumulated at the Upsilon(4S) by the CLEO-II detector, we report measurements of BR(B0 -> D*+ pi-) = (2.81 +/- 0.11 +/- 0.21 +/- 0.05) x 10^{-3} and BR(B- -> D*0 pi-) = (4.34 +/- 0.33 +/- 0.34 +/- 0.18) x 10^{-3}.
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