Using 106 $times 10^{6}$ $psi^{prime}$ decays collected with the BESIII detector at the BEPCII, three decays of $chi_{cJ}$ ($J=0,1,2$) with baryon pairs ($llb$, $ssb$, $SSB$) in the final state have been studied. The branching fractions are measured to be $cal{B}$$(chi_{c0,1,2}rightarrowLambdabarLambda) =(33.3 pm 2.0 pm 2.6)times 10^{-5}$, $(12.2 pm 1.1 pm 1.1)times 10^{-5}$, $(20.8 pm 1.6 pm 2.3)times 10^{-5}$; $cal{B}$$(chi_{c0,1,2}rightarrowSigma^{0}barSigma^{0})$ = $(47.8 pm 3.4 pm 3.9)times 10^{-5}$, $(3.8 pm 1.0 pm 0.5)times 10^{-5}$, $(4.0 pm 1.1 pm 0.5) times 10^{-5}$; and $cal{B}$$(chi_{c0,1,2}rightarrowSigma^{+}barSigma^{-})$ = $(45.4 pm 4.2 pm 3.0)times 10^{-5}$, $(5.4 pm 1.5 pm 0.5)times 10^{-5}$, $(4.9 pm 1.9 pm 0.7)times 10^{-5}$, where the first error is statistical and the second is systematic. Upper limits on the branching fractions for the decays of $chi_{c1,2}rightarrowSigma^{0}barSigma^{0}$, $Sigma^{+}barSigma^{-}$, are estimated to be $cal{B}$$(chi_{c1}rightarrowSigma^{0}barSigma^{0}) < 6.2times 10^{-5}$, $cal{B}$$(chi_{c2}rightarrowSigma^{0}barSigma^{0}) < 6.5times 10^{-5}$, $cal{B}$$(chi_{c1}rightarrowSigma^{+}barSigma^{-}) < 8.7times 10^{-5}$ and $cal{B}$$(chi_{c2}rightarrowSigma^{+}barSigma^{-}) < 8.8times 10^{-5}$ at the 90% confidence level.
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