We report a study of the processes e+e-→J/ψD(*)D̄(*). In J/ψD*D̄* we observe a significant enhancement in the D*D̄* invariant mass spectrum, which we interpret as a new charmoniumlike state and denote X(4160). The X(4160) parameters are M=(4156-20+25±15)MeV/c2 and Γ=(139-61+111±21)MeV. We also report a new measurement of the X(3940) mass and width: M=(3942-6+7±6) MeV/c2 and Γ=(37-15+26±8)MeV. The analysis is based on a 693fb-1 data sample recorded near the Υ(4S) resonance by the Belle detector at the KEKB asymmetric-energy collider.