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Using (2712.4 +/- 14.3) x 10(6) psi(3686) events collected by the BESIII detector operating at the BEPCII collider, we present the first observations of the decays chi(cJ) (J = 0, 1, 2) -> p (p) over bar eta pi(0). Their decay branching fractions are determined to be B(chi(c0) -> p (p) over bar eta pi(0)) = (2.42 +/- 0.07 +/- 0.19) x 10(-4), B(chi(c1) -> p (p) over bar eta pi(0)) = (1.95 +/- 0.05 +/- 0.12) x 10(-4), and B(chi(c2) -> p (p) over bar eta pi(0)) = (1.33 +/- 0.05 +/- 0.08) x 10(-4), where the first uncertainties are statistical and the second systematic.