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 Ξ−b→Λ0bπ−. 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 fΞ−bfΛ0bB(Ξ−b→Λ0bπ−)=(5.7±1.8+0.8−0.9)×10−4,where fΞ−b and fΛ0b are the b→Ξ−b and b→Λ0b fragmentation fractions, and B(Ξ−b→Λ0bπ−) is the branching fraction. Assuming fΞ−b/fΛ0b is bounded between 0.1 and 0.3, the branching fraction B(Ξ−b→Λ0bπ−) would lie in the range from (0.57±0.21)% to (0.19±0.07)%.