  We calculate the masses of $\chi_{\rm c}(3P)$ states with threshold
corrections in a coupled-channel model. The model was recently applied to the
description of the properties of $\chi_{\rm c}(2P)$ and $\chi_{\rm b}(3P)$
multiplets [Phys.\ Lett.\ B {\bf 789}, 550 (2019)]. We also compute the
open-charm strong decay widths of the $\chi_{\rm c}(3P)$ states and their
radiative transitions. According to our predictions, the $\chi_{\rm c}(3P)$
states should be dominated by the charmonium core, but they may also show small
meson-meson components. The $X(4274)$ is interpreted as a $c \bar c$ $\chi_{\rm
c1}(3P)$ state. More informations on the other members of the $\chi_{\rm
c}(3P)$ 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.
