  The decays $\chi_{cJ}\to\Sigma^{0}\bar{p}K^{+}+{\rm c.c.}~(J = 0, 1, 2)$ are
studied via the radiative transition $\psi(3686)\to\gamma\chi_{cJ}$ 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
$\chi_{cJ}\to\Sigma^{0}\bar{p}K^{+}+{\rm c.c.}~(J = 0, 1, 2)$ are measured to
be $(3.03 \pm 0.12\pm 0.15)\times10^{-4}$, $(1.46 \pm 0.07\pm
0.07)\times10^{-4}$, and $(0.91 \pm 0.06\pm 0.05)\times10^{-4}$, 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.
