  Recently, the LHCb Collaboration has confirmed the state $X(4140)$, with a
mass $M=4146.5\pm 4.5^{+4.6}_{-2.8}$~MeV, and a much larger width
$\Gamma=83\pm21^{+21}_{-14}$~MeV than the previous experimental measurements,
which has confused the understanding of its nature. We will investigate the
possibility of the $\chi_{c1}(3P)$ interpretation for the $X(4140)$,
considering the mass spectra predicted in the quark model, and the strong decay
properties within the $^3P_0$ model. We also predict the strong decay
properties of the charmonium states $\chi_{c0}(3P)$ and $\chi_{c2}(3P)$. Our
results show that the $X(4140)$ state with the small width given in PDG can be
explained as the charmonium state $\chi_{c1}(3P)$ in the $^3P_0$ model, and
high precision measurement of the width of the $X(4140)$ is crucial to
understand its nature.
