We report the observation of the X(3823) state in the process e+e-→π+π-X(3823)→π+π-γχc1 with a statistical significance of 6.2σ, in data samples at center-of-mass energies sqrt[s]=4.230, 4.260, 4.360, 4.420, and 4.600 GeV collected with the BESIII detector at the BEPCII electron positron collider. The measured mass of the X(3823) state is (3821.7±1.3±0.7) MeV/c2, where the first error is statistical and the second systematic, and the width is less than 16 MeV at the 90% confidence level. The products of the Born cross sections for e+e-→π+π-X(3823) and the branching ratio B[X(3823)→γχc1,c2] are also measured. These measurements are in good agreement with the assignment of the X(3823) state as the ψ(1 3D2) charmonium state.