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By analyzing (27.12 +/- 0.14) x 10(8) psi(3686) events collected with the BESIII detector operating at the BEPCII collider, the decays chi(cJ) -> p (p) over barK(S)(0)K(-)pi(+) + c.c. (J = 0, 1, 2) are observed for the first time with statistical significances greater than 10 sigma. The branching fractions of these decays are determined to be B(chi(c0) -> p (p) over barK(S)(0)K(-)pi(+) + c.c.) = (2.61 +/- 0.27 +/- 0.32) x 10(-5), B(chi(c1) -> p (p) over barK(S)(0)K(-)pi(+) + c.c.) = (4.16 +/- 0.24 +/- 0.46) x 10(-5), and B(chi(c2) -> p (p) over barK(S)(0)K(-)pi(+) + c.c.) = (5.63 +/- 0.28 +/- 0.46) x 10(-5), respectively. The processes chi(c1,2) -> (p) over bar Lambda(1520)K-S(0)pi+ + c.c. are also observed, with statistical significances of 5.7 sigma and 7.0 sigma, respectively. Evidence for chi(c0) -> (p) over bar Lambda(1520)K-S(0)pi+ + c.c. is found with statistical significances of 3.3 sigma. The corresponding branching fractions are determined to be B chi(c0) -> (p) over bar Lambda(1520)K-S(0)pi+ + c.c. = (1.61(-0.64)(+0.68) +/- 0.23) x 10(-5), B chi(c1) -> (p) over bar Lambda(1520)K-S(0)pi+ + c.c.) = (4.06(-0.76)(+0.80) +/- 0.52) x 10(-5), and B(chi(c2) -> (p) over bar Lambda(1520)K-S(0)pi+ + c.c.) = (4.09(-0.84)(+0.87) +/- 0.42) x 10(-5). Here, the first uncertainties are statistical and the second ones are systematic.