We report the observation of a near-threshold enhancement in the omegaJ/psi invariant mass distribution for exclusive B-->KomegaJ/psi decays. The results are obtained from a 253 fb(-1) data sample that contains 275 x 10(6) BB pairs that were collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e(+)e(-) collider. The statistical significance of the omegaJ/psi mass enhancement is estimated to be greater than 8sigma.