  Using E1 radiative transitions $\psi(3686) \to \gamma\chi_{cJ}$ from a sample
of $(448.1 \pm 2.9)\times10^{6}$ $\psi(3686)$ events collected with the BESIII
detector, the decays $\chi_{cJ}\to \Sigma^{+}\bar{p}K_{S}^{0}+c.c.~(J = 0, 1,
2)$ are studied. The decay branching fractions are measured to be
$\mathcal{B}(\chi_{c0}\to \Sigma^{+}\bar{p}K_{S}^{0}+c.c.) = (3.52 \pm 0.19\pm
0.21)\times10^{-4}$, $\mathcal{B}(\chi_{c1}\to \Sigma^{+}\bar{p}K_{S}^{0}+c.c.)
= (1.53 \pm 0.10\pm 0.08)\times10^{-4}$, and $\mathcal{B}(\chi_{c2}\to
\Sigma^{+}\bar{p}K_{S}^{0}+c.c.) = (8.25 \pm 0.83 \pm 0.49)\times10^{-5}$,
where the first and second uncertainties are the statistical and systematic
ones, respectively. No evident intermediate resonances are observed in the
studied processes.
