We report the first observation of the charmless two-body mode B+/- --> omegaK(+/-) decay, and a new measurement of the branching fraction for the B+/- --> omegapi(+/-) decay. The measured branching fractions are B(B+/- --> omegaK(+/-)) = (9.2(-2.3)(+2.6) +/-1.0) x 10(-6) and B(B+/- --> omegapi(+/-)) = (4.2(-1.8)(+2.0) +/- 0.5) x 10(-6). We also measure the partial rate asymmetry of B+/- --> omegaK(+/-) decays and obtain A(CP) = -0.21 +/- 0.28 +/- 0.03. The results are based on a data sample of 29.4 fb(-1) collected on the Y(4S) resonance by the Belle detector at the KEKB e(+)e(-) collider
