The first study is presented of CP violation with an amplitude analysis of the Dalitz plot of B0→DK+π- decays, with D→K+π-, K+K-, and π+π-. The analysis is based on a data sample corresponding to 3.0 fb-1 of pp collisions collected with the LHCb detector. No significant CP violation effect is seen, and constraints are placed on the angle γ of the unitarity triangle formed from elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated with the B0→DK∗(892)0 decay are determined for the first time. These measurements can be used to improve the sensitivity to γ of existing and future studies of the B0→DK∗(892)0 decay.