Using 106 ×106 ψ′ decays collected with the BESIII detector at the BEPCII, three decays of χcJ (J=0,1,2) with baryon pairs ($\llb$, $\ssb$, $\SSB$) in the final state have been studied. The branching fractions are measured to be B(χc0,1,2→ΛΛˉ)=(33.3±2.0±2.6)×10−5, (12.2±1.1±1.1)×10−5, (20.8±1.6±2.3)×10−5; B(χc0,1,2→Σ0Σˉ0) = (47.8±3.4±3.9)×10−5, (3.8±1.0±0.5)×10−5, (4.0±1.1±0.5)×10−5; and B(χc0,1,2→Σ+Σˉ−) = (45.4±4.2±3.0)×10−5, (5.4±1.5±0.5)×10−5, (4.9±1.9±0.7)×10−5, where the first error is statistical and the second is systematic. Upper limits on the branching fractions for the decays of χc1,2→Σ0Σˉ0, Σ+Σˉ−, are estimated to be B(χc1→Σ0Σˉ0)<6.2×10−5, B(χc2→Σ0Σˉ0)<6.5×10−5, B(χc1→Σ+Σˉ−)<8.7×10−5 and B(χc2→Σ+Σˉ−)<8.8×10−5 at the 90% confidence level.