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Using 106 $\times 10^{6}$ $\psi^{\prime}$ decays collected with the BESIIIdetector at the BEPCII, three decays of $\chi_{cJ}$ ($J=0,1,2$) with baryonpairs ($\llb$, $\ssb$, $\SSB$) in the final state have been studied. Thebranching fractions are measured to be$\cal{B}$$(\chi_{c0,1,2}\rightarrow\Lambda\bar\Lambda) =(33.3 \pm 2.0 \pm2.6)\times 10^{-5}$, $(12.2 \pm 1.1 \pm 1.1)\times 10^{-5}$, $(20.8 \pm 1.6 \pm2.3)\times 10^{-5}$;$\cal{B}$$(\chi_{c0,1,2}\rightarrow\Sigma^{0}\bar\Sigma^{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}$$(\chi_{c0,1,2}\rightarrow\Sigma^{+}\bar\Sigma^{-})$ = $(45.4 \pm 4.2\pm 3.0)\times 10^{-5}$, $(5.4 \pm 1.5 \pm 0.5)\times 10^{-5}$, $(4.9 \pm 1.9\pm 0.7)\times 10^{-5}$, where the first error is statistical and the second issystematic. Upper limits on the branching fractions for the decays of$\chi_{c1,2}\rightarrow\Sigma^{0}\bar\Sigma^{0}$, $\Sigma^{+}\bar\Sigma^{-}$,are estimated to be $\cal{B}$$(\chi_{c1}\rightarrow\Sigma^{0}\bar\Sigma^{0}) <6.2\times 10^{-5}$, $\cal{B}$$(\chi_{c2}\rightarrow\Sigma^{0}\bar\Sigma^{0}) <6.5\times 10^{-5}$, $\cal{B}$$(\chi_{c1}\rightarrow\Sigma^{+}\bar\Sigma^{-}) <8.7\times 10^{-5}$ and $\cal{B}$$(\chi_{c2}\rightarrow\Sigma^{+}\bar\Sigma^{-})< 8.8\times 10^{-5}$ at the 90% confidence level.

Measurements of Baryon Pair Decays of $\chi_{cJ}$ Mesons