The first observation of the decays J/ψ→p¯ς+KS0 and J/ψ→pς¯-KS0 is reported using (10087±44)×106 J/ψ events recorded by the BESIII detector at the BEPCII storage ring. The branching fractions of each channel are determined to be B(J/ψ→p¯ς+KS0)=(1.361±0.006±0.025)×10-4, and B(J/ψ→pς¯-KS0)=(1.352±0.006±0.025)×10-4. The combined result is B(J/ψ→p¯ς+KS0+c.c.)=(2.725±0.009±0.050)×10-4, where the first uncertainty is statistical and the second systematic. The results presented are in good agreement with the branching fractions of the isospin partner decay J/ψ→pK-ς¯0+c.c.