The decays $chi_{cJ}toSigma^{0}bar{p}K^{+}+{rm c.c.}~(J = 0, 1, 2)$ are studied via the radiative transition $psi(3686)togammachi_{cJ}$ based on a data sample of $(448.1 pm 2.9)times10^{6}$ $psi(3686)$ events collected with the BESIII detector. The branching fractions of $chi_{cJ}toSigma^{0}bar{p}K^{+}+{rm c.c.}~(J = 0, 1, 2)$ are measured to be $(3.03 pm 0.12pm 0.15)times10^{-4}$, $(1.46 pm 0.07pm 0.07)times10^{-4}$, and $(0.91 pm 0.06pm 0.05)times10^{-4}$, respectively, where the first uncertainties are statistical and the second are systematic. In addition, no evident structure is found for excited baryon resonances on the two-body subsystems with the limited statistics.