We report an observation of the decay B{0}-->D{*-}tau{+}nu{tau} in a data sample containing 535x10{6} BB pairs collected with the Belle detector at the KEKB asymmetric-energy e{+}e{-} collider. We find a signal with a significance of 5.2sigma and measure the branching fraction B(B{0}-->D{*-}tau{+}nu{tau})=(2.02{-0.37}{+0.40}(stat)+/-0.37(syst))%. This is the first observation of an exclusive B decay with a b-->ctaunu{tau} transition.