  Using $(106.41\pm 0.86) \times 10^{6}$ $\psi(3686)$ events collected with the
BESIII detector at BEPCII, we study for the first time the decay
$\chi_{cJ}\to\eta'K^+K^-$, where $\eta'\to\gamma\rho^{0}$ and
$\eta'\to\eta\pi^+\pi^-$. A partial wave analysis in the covariant tensor
amplitude formalism is performed for the decay $\chi_{c1}\to\eta'K^+K^-$.
Intermediate processes $\chi_{c1}\to\eta' f_0(980)$, $\chi_{c1}\to\eta'
f_0(1710)$, $\chi_{c1}\to\eta' f_2'(1525)$ and $\chi_{c1}\to
K^*_0(1430)^{\pm}K^{\mp}$ ($K^*_0(1430)^{\pm}\to\eta' K^{\pm}$) are observed
with statistical significances larger than 5$\sigma$, and their branching
fractions are measured.
