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Using 9.67 x 10^6 BBbar pairs collected with the CLEO detector, we obtain the branching fractions BR(B^- --> D^0 pi^- =3D (49.7 +/- 1.2 +/- 2.9 +/- 2.2) x 10^{-4} and BR(Bbar^0 --> D^+ pi^- =3D (26.8 +/- 1.2 +/- 2.4 +/- 1.2) x 10^{-4}. The first error is statistical, the second is systematic, and the third is due to the experimental uncertainty on the production ratio of charged and neutral B mesons in Upsilon(4S) decays. 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