We perform a full amplitude analysis of the process e(+)e(-)-> J/psi D (D) over bar, where D refers to either D-0 or D+. A new charmoniumlike state X*(3860) that decays to D (D) over bar is observed with a significance of 6.5 sigma. Its mass is (3862(-32)(+26) (+40)(-13) )MeV= c(2), and its width is (201(-67) (+154)(-82) (+88)) MeV. The J(PC) = 0(++) hypothesis is favored over the 2(++) hypothesis at the level of 2.5s. The analysis is based on the 980 fb(-1) data sample collected by the Belle detector at the asymmetric-energy e(+)e(-)collider KEKB.