We report the first observation of a charmoniumlike state recoiling from the J/psi in the inclusive process e+e- -->J/psi+anything at a mass of (3.943+/-0.006+/-0.006) GeV/c{2}. We also observe the decay of this state into D*D[over ] and determine its intrinsic width to be less than 52 MeV/c{2} at the 90% C.L. These results are obtained from a 357 fb{-1} data sample collected with the Belle detector near the Upsilon(4S) resonance, at the KEKB asymmetric-energy e+e- collider.