Using E1 radiative transitions $psi(3686) to gammachi_{cJ}$ 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 $mathcal{B}(chi_{c0}to Sigma^{+}bar{p}K_{S}^{0}+c.c.) = (3.52 pm 0.19pm 0.21)times10^{-4}$, $mathcal{B}(chi_{c1}to Sigma^{+}bar{p}K_{S}^{0}+c.c.) = (1.53 pm 0.10pm 0.08)times10^{-4}$, 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.