We calculate the masses of chi _{mathrm{c}}(3P) states with threshold corrections in a coupled-channel model. The model was recently applied to the description of the properties of chi _{mathrm{c}}(2P) and chi _{mathrm{b}}(3P) multiplets (Ferretti and Santopinto in Phys Lett B 789:550, 2019]. We also compute the open-charm strong decay widths of the chi _{mathrm{c}}(3P) states and their radiative transitions. According to our predictions, the chi _{mathrm{c}}(3P) states should be dominated by the charmonium core, but they may also show small meson-meson components. The X(4274) is interpreted as a c {{bar{c}}}chi _{mathrm{c1}}(3P) state. More information on the other members of the chi _{mathrm{c}}(3P) multiplet, as well as a more rigorous analysis of the X(4274)’s decay modes, are needed to provide further indications on the quark structure of the previous resonance.