We report observations of CP violation in the decays B(0) --> K(+)pi(-) and B(0) --> pi(+)pi(-) in a sample of 383 x 10(6) Upsilon(4S) --> BB[over] events. We find 4372+/-82 B(0) --> K(+)pi(-) decays and measure the direct CP-violating charge asymmetry A(Kpi) = -0.107+/-0.018(stat)(-0.004)(+0.007)(syst), which excludes the CP-conserving hypothesis with a significance of 5.5 standard deviations. In the same sample, we find 1139+/-49 B(0) --> pi(+)pi(-) decays and measure the CP-violating asymmetries S(pipi) = -0.60+/-0.11(stat)+/-0.03(syst) and C(pipi) = -0.21+/-0.09(stat)+/-0.02(syst). CP conservation in B(0) --> pi(+)pi(-) (S(pipi) = C(pipi) = 0) is excluded at a confidence level 1-C.L. = 8 x 10(-8), corresponding to 5.4 standard deviations.