We report the first observation of the decay B(0)-->D(+/-)D(*-/+) with the Belle detector at the KEKB e(+)e(-) Collider operated at the Upsilon(4S) resonance. The sum of branching fractions B(B(0)-->D(+)D(*-))+B(B(0)-->D(-)D(*+)) is measured to be (1.17+/-0.26(+0.22)(-0.25))x10(-3) using the full reconstruction method where both charmed mesons from B0 decays are reconstructed. A consistent value [(1.48+/-0.38(+0.28)(-0.31))x10(-3)] is obtained using a partial reconstruction technique that uses only the slow pion from the D(*-)-->D(-0)pi(-) decay and a fully reconstructed D(+) to reconstruct the B(0).