The CP violation observables S and C in the decay channel B0 → DþD− are determined from a sample of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 3 fb−1. The observable S describes CP violation in the interference between mixing and the decay amplitude, and C parametrizes direct CP violation in the decay. The following values are obtained from a flavor-tagged, decay-time-dependent analysis: S ¼ −0.54þ0.17 −0.16 ðstatÞ 0.05ðsystÞ, C ¼ 0.26þ0.18 −0.17 ðstatÞ 0.02ðsystÞ. These values provide evidence for CP violation at a significance level of 4.0 standard deviations. The phase shift due to higher-order standard model corrections is constrained to a small value of Δϕ ¼ −0.16þ0.19 −0.21 rad.