We perform a full amplitude analysis of the process e+e-→J/ψDD, where D refers to either D0 or D+. A new charmoniumlike state X∗(3860) that decays to DD is observed with a significance of 6.5σ. Its mass is (3862-32+26 -13+40) MeV/c2, and its width is (201-67+154 -82+88) MeV. The JPC=0++ hypothesis is favored over the 2++ hypothesis at the level of 2.5σ. The analysis is based on the 980 fb-1 data sample collected by the Belle detector at the asymmetric-energy e+e- collider KEKB.