We report on a search for (B) over bar (0) --> D-(*()0)(K) over bar (()*()0) decays based on 85 x 10(6) B (B) over bar events collected with the Belle detector at KEKB. The (B) over bar (0)-->D-0(K) over bar (0) and (B) over bar (0) --> D-0(K) over bar*(0) decays have been observed for the first time with the branching fractions B((B) over bar (0)-->D-0(K) over bar (0))=(5.0(-1.2)(+1.3) +/- 0.6) x 10(-5) and B((B) over bar (0) --> D-0(K) over bar*(0)) = (4.8(-1.0)(+1.1) +/- 0.5) x 10(-5). No significant signal has been found for the (B) over bar (0) --> D*(0)(K) over bar (()*()0) and (B) over bar (0)-->(D) over bar (()*()0)(K) over bar*(0) decay modes, and upper limits at 90% C.L. are presented.