Abstract: Using a pp collision data sample corresponding to an integrated luminosity of 3.0 fb(-1), collected by the LHCb detector, we present the first search for the strangeness-changing weak decay Xi(-)(b) -> Delta(0)(b)pi(-). No b hadron decay of this type has been seen before. A signal for this decay, corresponding to a significance of 3.2 standard deviations, is reported. The relative rate is measured to be f Xi(-)(b)/f Lambda B-0(b)(Xi(-)(b) -> Lambda(0)(b)pi(-)) = (5.7 +/- 1.8(-0.9)(+0.8)) x 10(-4) where f Xi(-)(b) and f Lambda(0)(b) are the b -> Xi(-)(b) and b -> Lambda(0)(b) fragmentation fractions, and B(Xi(-)(b) -> Lambda(0)(b)pi(-)) is the branching fraction. Assuming f Xi(-)(b)/f Lambda(0)(b) is bounded between 0.1 and 0.3, the branching fraction B(Xi(-)(b) -> Lambda(0)(b)pi(-)) would lie in the range from (0.57 +/- 0.21)% to (0.19 +/- 0.07)%.