We present new measurements of branching fractions for the color-favored decays B + → D 0π - and B̄ 0 → D +π -. Using 9.67×10 6 BB̄ pairs collected with the CLEO detector, we obtain the branching fractions Β(B - → D 0π - = (49.7±1.2±2.9±2.2)×10 4 and Β(B̄ 0 → D +π -) = (26.8±1.2±2.4±1.2)×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 Y(4S) decays. These results, together with the current world average for the color-suppressed branching fraction Β(B̄ + → D 0π 0), are used to determine the cosine of the strong phase difference δ I between the I = 1/2 and I=3/2 isospin amplitudes. We find cos δ I = 0.863 -0.023-0.035-0.030 +0.024+0.036+0.038, and obtain a 90% confidence interval of 16.5° < δ I < 38.1°. This nonzero value of δ I suggests the presence of final state interactions in the D π system.