A search for previously unobserved decays of beauty baryons to the final states K(s)(0)p pi(-) and K(s)(0)pK(-) is reported. The analysis is based on a data sample corresponding to an integrated luminosity of 1.0 fb(-1) of pp collisions. The Lambda(0)(b) -> (K) over bar0 p pi(-) decay is observed with a significance of 8.6 sigma, with branching fraction B(Lambda(0)(b) -> (K) over bar0 p pi(-)) = (1.26 +/- 0.19 +/- 0.09 +/- 0.34 +/- 0.05) x 10(-5,) where the uncertainties are statistical, systematic, from the ratio fragmentation fractions f Lambda(0)(b)/fd, and from the branching fraction of the B-0 -> K-0 pi(+)pi(-) normalisation channel, respectively. A first measurement is made of the CP asymmetry, giving A(CP)(Lambda(0)(b) -> (K) over bar0 p pi(-)) = 0.22 +/- 0.13 (stat) +/- 0.03 (syst). No significant signals are seen for Lambda(0)(b) -> K(s)(0)pK(-) decays, Xi(0)(b) decays to both the K(s)(0)p pi(-) and K(s)(0)pK(-) final states, and the Lambda(0)(b) -> D-s(-)(-> (KsK-)-K-0)p decay, and upper limits on their branching fractions are reported.