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 Ξb-→Λb0π-. 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 fΞb-fΛb0B(Ξb-→Λb0π-)=(5.7±1.8-0.9+0.8)×10-4,where fΞb- and fΛb0 are the b→Ξb- and b→Λb0 fragmentation fractions, and B(Ξb-→Λb0π-) is the branching fraction. Assuming fΞb-/fΛb0 is bounded between 0.1 and 0.3, the branching fraction B(Ξb-→Λb0π-) would lie in the range from (0.57±0.21)% to (0.19±0.07)%.